If it's not something mechanical like a broken spring letting it fall I'd unplug and replug the connectors on your driver board next. (It's almost got to be something like a bad or stuck switch though).

http://www.pinrepair.com/sys11/index1.htm#trans

Read the part about "Special Solenoids"

the Special solenoids have yet another switch involved. This is the scoring switch, which is part of the switch matrix (unlike the special solenoid trigger switch). So each pop bumper and slingshot have a second physical switch mounted on the playfield device. This switch closes as the coil energizes. This switch matrix switch in turns tells the CPU to score the device (but does *not* tell the CPU to fire the coil). So if there's a pop bumper or slingshot that works fine (energizes), but does not score, often it's because this secondary switch matrix switch is mis-adjusted or broken.

I'd suspect the 6821 PIA first now. I just talked privately to someone about those today. At least try socketing and swapping them if you want before replacing. There are several on the old williams driver boards that deal with switches, lamps, solenoids. etc.

This is where a logic probe or like the old logic LED clip comes in handy we talked about in a thread a few weeks ago.

Being so intermittent don't rule out just a bad connector or connection right away. IC's usually don't go bad this way but it is an outside chance. Socket and swap them first before spending money on new ones.

If even a tiny bit of acid corrosion got in that connection it could cause it to short and in this case continually fire.

Do you have tools to probe the PIA? I have never heard about this problem before. Locked on coils, okay, but coils that keep firing repeatedly? Are you sure it's not a problem in the switch matrix, did you try to start the game with the switches connector disconnected from the cpu or interconnect board?

With the intermittent nature I tend to lean more towards the acid damage. As a cheap repair I would cut the trace on the board and run a jumper from the connector to the PIA chip pin that drives it.

Have you already tried to "kick" and shake the machine to see if the pop bumper fires when the game is vibrated? I know that this sort thing happens with slingshots quite frequently, when their switches are set too tight.

I would also suggest you try to disconnect the switches connector (I think that's the one with the white wires) and see if the prob still occurs. We'll need to make sure the problem is not caused by some phantom switch. By the way, a broken switch diode could also be the culprit here.