Appends or Prepends? Depends
Jelly, 33 32 37 35 34 bytes

bug found, horrible fix +5 bytes, better fix - 2 bytes, using a trick of Adnan's I saw here for -1 more.

“({[&lt;“)}]&gt;”Z;@WœṣF¥/µÐLO‘&amp;2µIṀ&gt;0ȯQ


Return values:

prepends [2]
 appends [0]
    both [2,0]
 neither 1


(Invalid input returns spurious results, although valid Brain-flack, returns [].)

Try it online! - a test suite (prints mushed representations, so 20 for [2,0], and ignores lines containing any -).