Because it is not a reproducible failure, it sometimes doesn’t happen for quite a while, the el.caps would pobably test ok.
Actually, they wouldn't (and I'm taliking about the smaller ones). I'd wager you'd have a small handfull that would have higher than normal ESR levels. I have a Creative Electronics ESR meter, and in old units like yours you can easily identify caps that are even partially dry. It is, after all, a 20 year old unit. More on this later.
2-6800mfd-WOW...that is an old unit.
You wiggle the relay and it comes on? The contacts are probably gutted.
Assuming you've checked your connection, and resoldered any cold solder joints, here's what I'd do:
replace the relay.
If that fixes it, and you don't have an ESR meter and care about about long term operation, you're all set.
If you're looking long term:
Take a shotgun (an old-time Tech term) approach:
You've only got about 10 small electrolytics? Replace them all. It's cheap enough.