Nothing. Uh, oh. I turned it off and tried again. The engine turned over and started with no problem at all as if the first non-event was a non-event.
I tried not to worry about this too much while dealing with the rest of my errands for Mom, but mentioned it to my sister and nephew at the end of the day. My nephew Shane, who has some knowledge here, said that it sounded like a stuck starter solenoid, and suggested that if it gets completely stuck to go bang on it with a hammer. Of course, it probably needs replacing, too.
This is almost the opposite of the distributor problem on the last Nevada trip, in that then the starter and battery were just fine but the engine wouldn't start.
Now I have to find a window of opportunity for my mechanic to have a look at it.