I've gone ahead and replaced rain module and all is well. (Never removed power from the ISS nor the console.)
I am still confused, though. I thought on the Vue ISS, the magnet on the module tripped a counter on the board, in which case this shouldn't have worked? I don't see anything wrong with the old bucket, it tips just fine. Very strange... but a less than $20 fix and I have rain measurements again, so confused but happy.