We had the windlass energized one day when we were doing some other maintenance, and the windlass turned itself on! At that moment we were taking a break below deck so there is no way we inadvertently turned it on. It came on in the "up-chain" mode. We left it on and two days later it did it again in the middle of the night.
It seems the most reasonable explanation is the "Up" button. The switch externally is not corroded, but the rubber cover is torn so it could have gotten moisture inside it to bridge the switch. I checked it with a multi-meter and it has a very fluky read, sometimes 5kohms button off and 23kohms button on, and sometimes "0.L" in both positions. That would make some sense if the button was internally corroded, but in neither case was there good continuity with the button off (it had to be in that position for the winch to come on...right?)
Internally all the windlass connections have grease on them (one assumes non-conductive) and appear in great condition (no corrosion). The down button had been replaced by Steve Leeds in early 2015.
Is there anything else that I should be checking?