I doubt that the tilt switch is grounding through the paper, unless that paper has become conductive. You can test that theory really quickly by wrapping the tilt in electrical tape or a piece of cardboard (just the one leg)

Is it tilting (ending ball) or slamming (ending game and resetting?) If it's just tilting the ball - that's not the tilt switch that's activating. The door switch will reset the game. Unfortunately, so will random resets from a bad boardset - usually the 40 pin interconnect, bad sockets, or suspect (AMI) chips (cpu or pias)

The tilt switch on the door is a slam tilt only unless someone has really messed with the wiring.

Reseating/pressing on connectors/chips will work for a while but it does point to the need to change suspect sockets and resolder or replace pins as needed. Might be fine for another 40 years, too, though.

I kind of like wiring them up to a credit switch instead then I can knock the door to put credits on the machine.

The Stellar Wars in my arcade growing up would award 5 credits for kicking the door when the slam tilt was maladjusted. I bet the arcade wondered why all these kids were playing that game all the time.... until they collected it and there was no money in it.

Most of mine I actually have wired for the coin return switch to hit an auxiliary switch in the door instead. I have the slams all disabled in most of the games so I'm not tempted to kick the doors when I'm having a bad game.... ironically, based on your username, all except on my black knight that one is active for a quick reset after it's handed me my ass.