Update:
I was having trouble getting the 210° On, 195° Off switch hot enough to trigger in a simple boiling water bath, so I went back to the bike. I attached the wire from the wiring loom to the switch terminal and grounded the body of the switch to the frame of the bike by running a heavy-duty jumper cable from there to the bare-metal passenger peg bracket.
I proceeded to gently warm the switch (now hanging in mid air) by waving a very low flame from a propane torch onto it while checking its temperature every few seconds with the non-contact thermometer. I couldn't check the temp with any real precision that way, but I got it between 210° and say, 250° at most. When tested this way, BOTH OLD AND NEW SWITCHES WORKED! The relay clicked and the fan came on. Letting the switch cool opened the circuit and the fan shut off.
A professional mechanic mate of mine suggested that the relay might have been the real source of the problem all along as in its 41-year life it had gotten "lazy" from dirt or simple lack of use (the bike only has 6000 miles on it). That feels plausible to me, and I'm hoping that all the extremely rapid open/close cycling of the relay hundreds of times during testing has shaken it out of its torpor for now.
Today I'll make sure the coolant reservoir is topped up, then run the bike up to temperature and see what happens!