Thanks for the suggestion. I think the device that seemed to be running was actually not the one in the small picture but on the opposite side of the hose, about opposite to the word "here" in the larger picture. Is that where the idle speed valve is located?

Unfortunately for diagnosis, although the symptom was still there after charging overnight (before I removed the charger), after I started the car up and drove it for a while, there was no symptom when I then shut the car off. I looked at the wires going into the switch I suspected, but didn't see any obvious problems.

I'd think a short in the ignition switch would show other symptoms, like the dash warning lights being on.

Intermittant electrical problems are a pain. If it happens again (and it probably will), I'll try to disconnect the plug and see if the vibration stops.