This is key. The crimps get tarnished (or corroded if the battery leaked) and can cause all sorts of problems.

ALSO: there are 3 relays under the playfield. All coil power goes through a normally closed switch on T and and normally open switch on Q. You should clean and adjust those to make sure the solenoid power switches aren't the problem.

Finally: the sound card uses coil power for the amplifier (don't quote me on this see pinwiki: https://www.pinwiki.com/wiki/index.php?title=Gottlieb_System_80#Sound.2FSpeech_Power_Supply_Board_LED.27s , https://www.pinwiki.com/wiki/index.php?title=Gottlieb_System_80#The_Long_and_Winding_Road_of_the_Sound_Signals). so 1 theory is the solenoid power is cutting out and then returning after something cools down. Next time it does it pop the backbox open and test this voltage on the power supply, the coils and the sound board aux power supply.

You said you repinned but didn't do any recrimps. That's only half the job

The other boards were replaced for a reason. It's likely they put the new boards in, nothing worked and they gave up. The switch connectors J5 & J6 and the interconnect should be done too but the playfield switch connector J6 is a common cause of problems as it's in the battery damage zone

This could be used to eliminate this board. Pull the connector and if it still happens then it's not the problem