| Is anything else loose, like the grip? The box doesn't care WHERE the break in the circuit is...loose barrel, loose grip, depressed tip...all the same to the box.
If everything's still tight, try this...hook up a test box to the weapon and remove the tip and spring...stick in a jewelers screwdriver and place the point on the wire cap, then lean the screw driver over until it touches the barrel...you should get a completed circuit light.
Keeping the screwdriver in contact with the wire cap, run the shaft of the screwdriver around the inside of the barrel, keeping contact at all times. if you still get the circuit breaking (meaning the light turns off), you probably have a broken wire at the base of the wire cup...and your white light comes from point movement pulling the broken ends apart, breaking the circuit.
Rewire time.
If that's not it, please describe IN DETAIL exactly what's going on when you get a white light...what kind of actions, blade contacts, etc.
Don't hold anything back...a trivial point of interest to you may be exactly what an armorer needs to hear. | 
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