I fixed it, finally. Kinda hard to explain what it was, but I've always had these two weird relays under the dash. They aren't factory, and my best guess is they somehow went with the air conditioning my bus used to have.
I traced all the wires coming from the headlight switch to where they were supposed to go. One of them was going to fuse number 7, where it was also jumpered to another wire that went to the strange relays. The thing was, there was no other wires going into fuse 7 and neither Nick nor I could locate on the wiring diagrams anything that was designated for fuse 7. So I guess somehow it was an "extra" that maybe dealers could use for accessories they installed, such as A/C. (The book says fuse 7 is for "accessories" too.)
That wire is supposed to be going to switched power, it energizes the headlight relay when the key is on. I moved it to fuse 10 which is switched power for windshield wipers and the rear defrost (which no longer works anyways). Now my headlights work as they should!
While I was in there, I took the opportunity to straighten out some more of the bad wiring. Turns out I had ran the hot wires for the radio, clock, and cigarette lighter off the wrong side of the fuse so they were not protected. I moved them and made everything under there much neater.
Also fixed my dome light, which turned out to be the bulb. For some reason I was thinking it was a wiring issue and never looked at it. I don't remember the last time she had a working dome light.
Zen, I have an extra good working (original) headlight switch. It's yours as soon as you get Homer running!