1968 fender twin questions

[HotBluePlates]

... Does moisture cause the boards to be conductive and if yes why won't running them drive that moisture out?

Yes, the fiberboards absorb moisture over a period of years. Eventually, the combination of the moisture and the carbon which dyes the board black leads to a conductive board. Or perhaps we should say a "leaky board" meaning the high resistance between eyelets is dropping (but maybe not far enough that you'd call it "conductive").

If you've been inside Fender amps older than this one, you'll notice the board in this amp has a waxy coating on it compared to older fiberboards. I don't know for sure, but suspect Fender did this to combat the moisture issue.