Panicked a little when I couldn't get the backup light to work with the trans in reverse (knowing the switch was good); thought maybe I had a bum transaxle.
Then I tried pushing the car a little in gear. Low and behold: the fan spun counterclockwise in both reverse and second!
I was able to fix it pretty quickly after that discovery.
Also spoke to the safety inspector guy today and he's pretty sure—not 100 percent, but pretty sure—he'll have to see working windscreen wipers to give the car a pass. So I'll be saddling up the glass screen and delving back into my long-abandoned wiper rig before putting the floor back on the car.
All in the game, I guess.