Thank you for the comments!
Mark, with the on/off functions it usually (but not always) takes two clicks to get it to switch to the other state. Occasionally one or three or four clicks.
Simon and Bob, it does sound like contact cleaner or air might help. And Bob, that is very interesting to know. Contact cleaner would make me nervous but air a bit less so... either would probably be made trickier by the weather sealing, I imagine.
VonB, interesting idea -- I don't have one of those, though.
APMII, I have been in touch with the seller, we both just thought we would cross our fingers and hope there was a simple solution that the Pentax hive mind might know about.
Happy to hear any other ideas or opinions.
---------- Post added 08-07-21 at 12:45 PM ----------
Oh, and Bob, to your sidenote -- this is the unlabeled top dial on the K-1 -- the third one -- not the rear panel's thumbwheel.