Thanks to all who replied. I’m back home for a few days and trying to get caught up on past work.
When I checked the ac system, it was low: the head pressure was just over 100 lbs, and the suction was also low, of course. When I brought the head pressure up to about 225 and the suction to about 35, the cooling fans turned on, so the fan switch was not faulty after all. I did notice that hot water was apparently circulating through the heater core. The diverting valve appears to be working, but I guess it is not shutting off altogether since the return hose was hot. So for the time being, I pinched the return hose shut to keep hot water out of the heater. All seems to be working well for the time being.
Again, thanks for the helpful information.