FOLLOWUP: Took the dash apart again and tested the following:
1. Multi-function switch. All continuity was good.
2. Input from dash switch voltage. 12 Volts as expected. Neither High nor low beams work
3. Input from Temp Hi beam. 12 Volts as expected. Temp Hi beam works.
OK. I tried using a small jumper wire on the plug to the headlight portion of the multi function switch. And got the following results:
1. Jump Dash switch to low beams. No Joy. Huh, this reads 12 volts with no load.
2. Jump Temp hi beam to low beam. It works.
So the line running from the dash switch holds 12 volts with no load but cannot pass any current. When jumped the voltage goes to zero.
We take apart the Main Dash headlight switch and find what appears to be a previous repair that required a whole new plug assembly. Each wire was attached with a crimped connector. The one for the headlights was real hot (to hot to touch). It visually looked OK and after jiggling it, it worked again. I cut it out and replaced with a new crimped connector. This one stayed cool after headlights on for 5 minutes.
I hope this is a good fix. It sounds like this 15 year old car (we own for less than 1 year) had, based on my reading of the forums, a common problem with the headlight wiring. This problem can result in a fried main headlight switch, connector, and some wiring. My problem was that the fix in my sons car also had a problem. Hopefully my fix will last a few years.