Zowie.
dailydose: I am so glad you wrote what you did. I decided to take off the cover again and let the kitchen fan do a bit of overnight work, only to discover that there was again water under the tank on its ledge and some more had leaked to below!
It was only then that I found an amazingly invisible hairline crack in the side of the water tank.
I have used superglue to seal the crack, and will test it overnight with some water inside to check for leaking.
I have re-hair dried the innards, will leave the fan on, and maybe check again sometime tomorrow.
wookie: I was afraid of that, but your caution will keep me from rushing.
cannonfodder: I'm looking for a small fan right now...
I really appreciate this forum and all three of you for the help.