After about an hour of tracing out the rather sketchy wiring diagram in my Haynes manual, and 45 minutes of testing the switch and the circuits, I determined that the headlight switch is defective - for mechanical reasons. The headlight switch is in two parts: a) a faceplate that carries the knob and b) the switch circuitry in a block that is held behind the face plate by tabs that snap into cross-wise slots (behind all that is the wire connector). The cross-wise slots at the bottom had broken out, and the circuit block was swinging free, and failing to make contact. This I did not discover until I'd ordered a replacement switch (eEuroparts, less than half the local discount auto parts store), but that's OK; I'd rather not depend on the duct tape currently jury-rigging the switch together.

Some notes:

1. The headlight circuit is insanely complex. As best I can tell, there are three relays to operate it, in what locations I don't know, so I'm glad that it was the switch (especially since those plug-in relays are really hard to test).
2. One of those relays turns on power to the headlights when the switch connects terminals 7 and 9. I determined that the problem was the switch when I was able to jumper across those two terminals and get lights, but testing the corresponding terminals on the switch did not show continuity, until I taped the switch together (feeling like a fool when I finally realized what had been screaming at me from the time I took the switch out and noticed it was kind of floppy).
3. The switch uses small-dimension male spade terminals going into spring-loaded female receivers in the connector. I didn't have any male spade terminals of that small dimension, so I cut strips of galvanized flashing, pushed them into the connector, and jumpered across them with a wire with alligator clips. Pieces of unpainted tin can would probably have worked as well, but I had the flashing.
4. As I mentioned, at the moment, the headlight switch is held together with duct tape. Not the plastic stuff, but a metallic tape that's the modern version. Very strong, very sticky, and would probably last another 50,000 miles; I may save the headlight switch when I replace it with the new one, as a spare.
5. The manual describes removing the switch (indeed, all the instrument panel switches) by prying at it with a little screwdriver. This is more than kind of a pain. I took a couple of pieces of the flashing about 1/2" wide and about 2" long, bent a sharp right angle on one end by doing a rough bend first, then clamping the length in the vise with the bent part at the jaw and hammering it to a sharp bend, and filed the resulting "finger" very short. So far, this seems to work better - I push the sheet metal back to catch the back lip of the front part of the switch and pull.