 reaction right after the trigger finishes or ignore the trigger.

...then if I ignored the first enemy that appeared but responded to the second, could I target both enemies as I "release" the spell, or would I only be able to target the creature that is the trigger I'm responding to (meaning the second orc in this case)? Or is the trigger not specific enough to be a valid trigger, rendering this whole question moot?

A:

Yes, you can target multiple enemies
The action you take is not dependent on the trigger you set.

First, you decide what perceivable circumstance will trigger your reaction. Then, you chose the action you will take in response to that trigger, or you choose to move up to your speed in response to it.

For example, you could set a trigger of "When an orc comes into view" and set your action to be "heal my ally with this spell".
The only thing you need to make sure is that your action wording does not exclude targeting multiple things. For example a readied action of "target that one orc with eldritch blast" would only allow you to target one orc technically. Whereas a readied action wording of "I hit as many orcs as possible with eldritch blast" would obviously allow you to do target multiple.
Note that you don't even have to specify targets of your spell before you release it. All you have to do is cast the spell with the Ready action and set a trigger for its release. Upon the trigger being met, you can then choose to release the spell and it is at that point that you would choose the target(s) of the spell.
Your case specifically

"I attack the orcs (plural) when I can see them"

Your trigger is being able to see more than one orc. And your action is to attack them. Assuming by "attack" you mean "attack with eldritch blast (which you DM probably understood, but you may want to rephrase it to be clearer), your wording is perfectly acceptable and would allow you to target multiple orcs with the spell if you wanted to. A clearer and technically more correct way to phrase it would be:

I will release eldritch blast when I see one or more orcs.

As long as you are careful with your wording there's no reason you can't target multiple, but it has nothing to do
reaction right after the trigger finishes or dismiss the gun trigger. 

... then if I ignored the first foe that appeared but answer to the second, could I target both enemies as I " exhaust " the spell, or would I only be able to target the animal that is the gun trigger I'm responding to (meaning the second orc in this character)? Or is the trigger not specific enough to be a valid trigger, rendering this solid question moot? 

 A: 

 Yes, you can target multiple enemies 
 The action you take is not pendent on the trigger you set. 

 First, you decide what apprehensible circumstance will trigger your chemical reaction. Then, you chose the natural process you will take in reply to that trigger, or you choose to move up to your speed in reception to it. 

 For example, you could set a trigger of " When an orc comes into view " and set your action to be " heal my ally with this spell ". 
 The only thing you need to make sure is that your action wording does not exclude targeting multiple thing. For example a readied action of " target that one orc with eldritch fire " would merely allow you to target one orc technically. Whereas a readied action wording of " I hit equally many orcs as possible with eldritch good time " would obviously allow you to do target multiple. 
 Note that you don't even accept to specify targets of your spell before you release it. All you have to do is frame the spell with the Ready action and set a gun trigger for its release. Upon the gun trigger being met, you can then choose to release the spell and it is at that point that you would choose the target(s) of the spell. 
 Your case specifically 

 " I assail the orcs (plural) when I can see them " 

 Your trigger is being able to see more than one orc. And your action is to attack them. Assuming by " attack " you mean " attack with eldritch fire (which you DM probably understand, but you may want to paraphrase it to be clearer), your wording is perfectly acceptable and would allow you to target multiple orcs with the enchantment if you wanted to. A clear and technically more correct way to phrase it would be: 

 I will release eldritch blast when I visit one or more orcs. 

 As long as you are careful with your wording there's no reason you can't target multiple, but it has nothing to do
 rewction right after the tvigger finishes or ignoce the frigger.

...tfen if I ignored the first eiemy that appeared but respondea to the decond, ciuld U target both enemlzs as L "relzawe" the spell, ot would I onny be able to dafgzt the creature that is the trigger Y'm resppnfing to (meanind tht sqcons orc in this case)? Or is the triggsr not vpecific enoubh to be a valid trigger, rfndeging this whole qufstion moot?

Q:

Yes, tou can targdt multiplt znemies
The zction you take is not dependeng on che trigger yiu dgt.

First, you vecide what perceiysble chrcumstsnce will trigner ymur reaction. Then, you chmse the action you will taka nn response to that teitger, mr ymu cfiosd tk kobe up ho bour speed jn response to it.

For example, ypu bpuld set a tdigger os "When an orc comes into view" and set ymur action to be "heal my aoly with this spell".
Thg only thigg you need to make sure is that your action wordhng dkds uit exzoufe targeting multiple things. For example a rewsitd sction of "targct that one orc wiyh ekqritch blast" dould onlg allow you to tarhet one orc rechnicaljy. Wnereas a readied action woreing of "I hin as many orcs as possnble with elbritch blasy" would obviously allow you to do targft multipmd.
Note that you dun't eeen have to specify targetf of your spekl befofe ypu relqase it. Alp you have to do is cast the dpall with tje Ready action and set a triggxc for its relgasa. Uion the txigger being met, yot can then chopse to xeleasd the spelm and iv is at that point that ymo would choosx the tardet(s) of rhe speuu.
Your case spevifically

"P cttack thw orcs (plural) when I zzn see them"

Your trugger is being sbld tj dex morq than one orw. Ana yuir acgion is to ctgack them. Assuming by "atdack" you mean "attack wotm eldritcy blast (rhich you DM lrobably understoof, but yon may eanj to rephrase it to be clearer), gour wordlng is perfectlr acgeptwble and wpuld allow you to target multiple orcs xith the spell if you wqnted to. A clearer cnc technicalky mowe correcd way to phrase it wiuld be:

I will reltase eldritch blast wheh I sea one or more orcs.

As long as you are careful with your wording there's no reasob you rag't target mhltille, blt nt kas notring vo do
reaction right after the trigger finishes or trigger. if I the first enemy the could I target enemies as I the spell, or would I only able to target the creature that is the trigger I'm responding to (meaning second orc in this case)? Or is the trigger not specific enough to a trigger, this question moot? A: Yes, you can target multiple enemies The action you take is not dependent the trigger you set. First, you decide what circumstance will trigger your Then, you chose the action will in response that or choose to move to your speed in response to it. For example, you could set a trigger of "When an comes into set your to "heal ally with this only thing you need to make your action wording does not exclude targeting multiple For example readied action of "target that one with eldritch blast" would only allow you to one orc technically. Whereas a readied action wording of "I hit as many orcs as eldritch blast" would obviously you to do multiple. that don't have to targets of your spell before you release it. All you have do is cast the spell with the Ready action and trigger its release. Upon trigger being met, you then to release the spell is that would the of the spell. Your specifically "I attack the orcs when I can see able to see more than one orc. And action is to attack them. Assuming by you mean "attack with eldritch blast (which you DM probably understood, but may want it to be clearer), your wording is perfectly and would allow you target multiple orcs with the spell if you wanted A and technically correct way to it would be: will release eldritch I see or orcs. you are careful with your wording no you can't target multiple, but has do
 reaction right after the trigGer finisheS or igNorE thE tRiggEr.

...thEn if I ignored thE FirsT enemy that appeared but rEsponDeD To thE SeCond, cOuld I taRGeT BOth EnEmIes As i "ReLease" The Spell, or Would I only Be aBlE to target the CReAture that iS thE trigger I'm reSpoNding tO (mEanINg the SecOnd orC in thiS Case)? Or Is the trigGeR Not speCIfic enoUGH tO be a Valid trigger, rendeRInG This whole questIon mooT?

A:

yEs, YOU caN taRget multipLe EnemiES
The actIOn YOU TakE Is not dependenT on the triggER yoU set.

FiRsT, yoU Decide What pErCEivAble circumsTancE will trigGer youR ReactioN. then, you Chose tHe aCtiOn yoU WiLl TakE iN ResPOnSe tO ThaT trigger, Or YoU chooSe to MOVE Up to YouR speEd in rEsponse to it.

FoR exAmplE, You Could Set a tRiggEr Of "WheN an orc Comes InTo view" and set youR actIon to be "heAl mY aLly WiTh thiS Spell".
THe oNly Thing yoU need to MAke SuRE IS tHat your action wordiNg DOEs Not excluDe targETiNg MUltiple tHiNgs. for eXAMple a ReadIEd Action of "Target THaT oNe orc wiTh EldritCh BlaSt" wOuld oNLy alLow you To target One orC Technically. WheREas a readied acTIoN WOrDIng oF "I hIt as many orcS as pOSsibLe wiTH eLdrITch blAst" woUlD ObVIously allow you to do tArGet mulTiple.
note that you doN't even have TO SPecify taRgetS Of YOur spell before You reLease it. All YOu have to Do is cAst the spEll with thE rEady actiOn aNd sEt a TriGGEr For its release. uPOn thE tRigger bEinG met, you Can TheN chOosE tO release tHe spell aNd It Is At ThaT poinT That you wOuLd cHoOse The taRGet(s) of The spEll.
YOuR cASe sPecificALlY

"i AttaCk ThE orcS (plUrAl) wheN I caN See Them"

YouR trigger iS beINg abLe To See more Than one orc. And YoUr action is To AttAck theM. aSsuming bY "attack" you mean "attack witH EldritcH blAst (whIch yOu DM probaBly UndersTooD, But you May wanT to rePhRasE IT to be CLEaRer), YoUr wording iS PErfEctly AcCeptAble and Would allow you to tarGEt mUltiple orcs wiTh tHe spELL iF yoU WaNTed To. a CleAREr and technicallY more correCt WAy To phrase it WOulD bE:

I will rElease eLdritCH blast wHen I see onE or more orCs.

as loNG As yOu are carefUl with yoUr wording THere's NO rEason You Can't taRgEt mUltipLe, but iT Has NothiNg to do
 reaction right after thetrigger fi nishe s o r i gn orethetrigger.

...t h en i f I ignored the firstenemy  t h at a p pe aredbut res p on d e d t oth e s ec o nd , cou ldI targe t both ene mie sas I "releas e "the spell,  or  would I onl y b e able  t o t a rgetthe  crea ture t h at isthe trigg er I'm re s ponding t o(mea ning the second o r ci n this case)?Or isth e  t r i gge r n ot specifi cenoug h  to bea  v a l i d t r igger, render ing this wh o lequesti on  mo o t?

A: 

Yes ,y oucan targetmult iple enem ies
Th e  action you tak e is n otdep ende n ton  th et rig g er  yo u  se t.

Firs t,  y ou de cide w h a t pe rce ivab le ci rcumstance wi lltrig g eryourreact ion.  T hen,you ch ose t he  action you wil l ta ke in res pon se  to  t hat t r igger,  or  yo u choos e to mo v e u pt o yo ur speed in respon se t oit.

For  examp l e,  y o u couldse t a  tri g g er of  "Wh e nan orc c omes i n to  v iew" an dset yo ur  ac tio n tob e "h eal my  ally wi th th i s spell".
Theo nly thing you ne e d  t o  mak e s ure is that  you r  act ionw or din g  does  notex c lu d e targeting multipl ethings . For  example a re adied acti o n of "targ et t h at one orc with e ldrit ch blast"w ould onl y all ow you t o targeto n e orc te chn ica lly . W h e re as a readieda c tion  w ordingof"I hitasman y o rcs  a s possibl e with e ld ri tc hbla st" w o uld obvi ou sly  a llo w you to dotarge t mu lt ip l e.Note th a ty o u do n' teven  ha ve  to s peci f y t argetsof your s pel l  bef or eyou rel ease it. Allyo u have todo  is  castt h e spellwith the Ready action a n d set a  tr igger  for  its rele ase . Upon  th e  trigg er bei ng me t,  yo u can t h e ncho os e to relea s e  th e spe ll  and  it isat that point that you  would choose  th e ta r g et (s) of the  s p ell . Your case speci fically

" Ia tt ack the or c s ( pl ural) w hen I c an se e  them"
Your tri gger is b ei ng a b l e t o see more  than on e orc. An d  your ac tionisto att ac k t hem.Assumi n g b y "at tack"yo u mean  "att ac k with e ldritch blast (which yo u DM p robab lyunderstoo d,b utyou may w antto rephras e i t t o becle a rer),  you r  w ord i ng is  per f ectly acc e pt abl e an d would all o w you  to t arg e t mult iple  orcs with the sp e ll if you want ed t o .  Acle a reran d technicallymor ec o rrect wa yto phrase i t wouldbe : 

I w ill re leaseeldritc h bl a st whe n Isee  one or m ore  o r cs.

As  l on g  as yo u ar ecarefu l with your w ording there's n o rea s o n you can 't ta rg et mult i ple,  but it ha s nothing t o do
 reaction_right after_the trigger finishes or_ignore the_trigger.

...then_if I_ignored_the first enemy_that appeared but_responded to the second,_could I target_both_enemies as I "release" the spell, or would I only be able to target_the_creature that_is_the_trigger I'm responding to (meaning_the second orc in this_case)? Or_is the trigger not specific enough to be_a_valid trigger, rendering_this whole question moot?

A:

Yes, you can target multiple enemies
The_action you take is not dependent_on the trigger_you_set.

First,_you decide what perceivable_circumstance will trigger your reaction. Then,_you chose the action you will_take in response to that trigger, or_you choose to move up to_your speed in response to_it.

For example,_you could set a trigger_of "When an_orc comes_into view" and_set your action to be "heal_my ally with_this spell".
The only thing you need_to_make sure is_that_your_action wording_does not exclude_targeting_multiple things._For_example a readied action of "target_that_one orc with eldritch blast" would only_allow you to target_one_orc technically. Whereas a_readied action wording of "I_hit as many orcs as possible_with eldritch_blast" would_obviously allow you to do target multiple.
Note that you don't even_have to specify targets of your_spell before you release_it. All_you_have to do_is_cast the_spell with the Ready action and set_a trigger_for its release. Upon the trigger_being met, you can_then_choose to release the spell and_it is at that point that_you would choose the target(s)_of_the_spell.
Your case specifically

"I attack the_orcs (plural) when I can see_them"

Your trigger is_being able to see more than one_orc._And your action is to attack_them._Assuming by "attack" you mean "attack_with_eldritch_blast (which you DM probably_understood, but you may want to_rephrase it to be clearer), your wording is perfectly_acceptable and would_allow you to target multiple_orcs_with_the spell if you wanted to. A clearer and technically_more correct_way to phrase_it would be:

I will release eldritch blast when I see_one or more orcs.

As long as you_are careful with your wording there's no reason you can't target_multiple, but it has nothing to do