How to mount a compact pump onto a full-suspension frame?
Electric tape is a bad idea because the adhesive can mess with your tube.

Other suggestions


Many off-road riders carry a hydration pack instead of bottles/bidons.  Carry your spares in the pack.
Jersey pockets have worked for roadies for many decades.
Do you have bottle cage mounts?  Either store your tools inside a bottle in the cage, or many mini pumps are sold with a mount point to go between the bottle cage and the frame.
I have a small triangular frame bag that fits inside the main diamond of my bike.  It carries tube and tools, and a USB battery to power the camera on longer rides.  It straps around the top and down tube by velcro.
Likewise you can use a top-tube bag, which velcro-straps to your top tube and around the steerer.  Often found with a clear plastic panel on top to hold your phone.  Sometimes referred ti as a Bento, because it can hold food for snacking. 
Not on your bike, but Time Trial bikes with Aerobars can have stuff mounted in the middle of the forearms, with relatively little aero impact.
Any sort of smallish cloth bag can carry your spares, and then use 2 or 3 velcro cable ties to fasten the bag to the frame where its out of the way, and not going to get dirty.  People who ride downhill would want the weight rear, so on the seatpost or seat.  Those who ride everything prefer weight low in the middle or forward if you do steep climbs.
Its also possible to load some tools inside handlebars, replacing the end plugs.  Although this can lead to accidental loss of tools and is no good for tubes.
I read somewhere that the latest Stumpjumper frame has storage compartments in the downtube, which sounds like an interesting idea.
There are frame pumps that are designed to wedge between a corner and a peg, but your frame probably won't have that.
Finally - consider not carrying it.   Instead you could carry a smaller CO2 inflator or add sealant to your tyres and trust it will do the job.  Not really recommended.  Further, there's little point carrying tools you can't use, don't fit your bike, or are broken/worn.  Weed out your loadout and take what you need not what you might need.
If you're out with mates, you don't all need a pump and a multitool.  Just stay together and avoid being separated.