Trap the ghost girl (Ghostbusters style) with the zap gun and throw a ghost trap at the ghost girl while she's zapped by the gun.
This is a fun idea. Not only would it make the zap gun more useful but a 2 item teamwork combo for trapping an enemy you can sell seems very silly and goofy.
As for the actual trap it could perhaps be used just like the ghost traps in ghost busters. As soon as she's zapped toss that bish right down in front of her or on her and activate it with a remote (which is included with the box item). This could perhaps just like the shotgun be a scrap item you find in late game facilities that you can sell or use for ghost busting.
Trapping the ghost girl in the box increases the box's value significantly.
A cool addition to this would be to be able to lure out the ghost girl with the various toy scrap items (like the toy robot or the hair dryer)