Well, thanks for the helpful suggestions.
I rebuilt all my cables with new ends and solder. I found it worked best to step up a size in the wiring eye. Solder on the wire, molten solder in the wiring eye, plus a tight fit was a recipe for frustration.
But the real news is that, when I pulled all the cables out and removed the battery switch, I thought to give it a little shake next to my ear, and I heard sloshing water! Impossible, I thought, how could water have gotten in there? I was absolutely certain that the switch had never been submerged. But finally I figured out that the position of the switch directly below a deck hatch meant that every time I hosed down the self-bailing deck, the switch was getting dripped on. Blindingly obvious mistake, in retrospect.
Anyway, with a new switch and better built cables I am back in business.
Here is a picture of the insides of the old switch. "Mystery" solved:
