It turns out that the fan mystery was a lot more simple than I had
suspected. The connector on the bottom of one of the fans is corroded,
and the clip that holds it on is broken off, so that the plug was not
not plugged in fully. A little piece of metal from the plug had come
off and stuck on one of the pins. I put a jumper from the battery to
the pins on the fan, and both fans ran.

I'll cut the old connector off of the wiring harness and graft on a new
one. That should settle the whole issue.

Thanks for all of your help.