Bill, I'm thinking you have a problem in the headlight system relay that's down by your feet. Silver cube on the firewall, inside the car under the dash. Mine, and many others, had a problem with poor connections at it burning the connector, and melting the wire, the connector, and the relay.
In my case, I was able to break the lead wire out of the fried connector plastic, and put it back together. My problem was that the lights wouldn't come on. But it is this relay that turns the whole thing on and off, including when you cycle the key to Start. The deal is, the ignition switch breaks contact to the accessories when you go from ON to START. Then it restores that connection as you release the key.

So if there's a short in the wiring at the relay, I guess I can see a way for it to continue energizing itself. If the relay coil wire is melted against the power out of the relay, that goes to the two fuses and the bulb out sensor and the high/low relay, then sure, you can have a situation like you describe.

Trust me, that relay can get HOT. Start your search there and let us know what you find!
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Rob Bareiss, New London CT ::: Roterande Fläkt Och Drivremmar!