I had occasional slam tilts on my JP. It was a switch matrix short as Crashdance22 stated. A standup target on the same row or column (can't remember which) was occasionally shorting out and causing the slam tilt.
I also had a slam tilt problem on a WWF RR. This was due to one of the 4011 NANDs for the switch return on the CPU board being bad. But it could be another component like the transistor Mike mentioned.
The difference between how the two problems behaved is that the JP matrix short would occur occasionally during gameplay when the target was hit just right. The WWF RR issue would happen even with the switch connectors (CN8, CN10) removed from the CPU board. Isolating the switches by removing the CN8 and CN10, and then manually triggering the matrix can help you determine if the problem is on the playfield or in the CPU.
Based on what you've reported, I'd do as Crashdance22 suggested and look at all the switches on the same row and column as the slam tilt switch. Look for shorts, solder splash making a short, wires out of place, etc.