Caps are cheap enough. I’d start by replacing them all and seeing if problem re presents itself. You could certainly bust out the schematic and start tracing paths and measuring voltages, but for me, I’d just recap the power and whatever else and see where I am then. Especially if the age of the caps is original or unknown. But I like soldering so each his own.

I’d start here: https://www.arcadepartsandrepair.com/store/components/williams-system-3-6-power-supply-105c-cap-kit/
The connectors prob 156, but someone else for sure knows. Some might say I’m shotgunning by doing it this way, but if the cap ages are unknown it’s best to get it done, then you can test board knowing you have clean caps.

Not seeing the picture.
Stock driver boards have some resistors which can get very hot.
Lots of issues come down to bad connectors, cracked solder on header pins, and the like.
Pinwiki.com has good repair info if you like to fix your own games.

The driver board always gets hot. As long as the game doesn't lock up it won't overheat. Those aren't capacitors on the driver board though, those are resistors. The red ones?

The capacitors on the power board won't help the heat the connector is generating. You need to fully replace both sides of that connector.

Sounds like your game is resetting, which could be a voltage issue, which recapping the power supply could fix. Replacing the lm323 voltage regulator can also help.

All the connectors on the hot tip boards are .156 inch. Best place to get all these parts would be great plains electronics. They'll have the header, pins, housing, and crimper, along with caps, etc

Those red resistors are in the lamp matrix. Frankly, yours look pretty good. I've seen far worse. They get pretty warm under normal operation but get really hot if the mpu quits running which is what it sounds like your game is doing. A primary suspect for that behavior is the 40-pin connector between the mpu and the driver boards - order those from GPE while you are at it. Definitely check out the basics for bullet proofing these games in the Pinwiki and Vid's Williams thread. Given that your capacitors still look original there are probably a hundred things you will need to do and most of it is fairly inexpensive and easy - just time consuming. Oh, and fun!