My gut feeling is that the ICP was slowly deteriorating, choking off the
current as the unit played, then "recovering" as it sat overnight.
Have you seen anything like that?

I've seen them go high resistance rather than totally open, but not
intermittently as far as I can recall. Are they the little TO92 style ones
?
If they've got an "N" number for the rating, I guess they are.

No, they're more like little rectangles than flattened cylinders.