89 headlight problem

There is a fault in the headlight circuit in my '89: The headlights come on with the headlight switch in the center and right positions even with the ignition turned off.
I have normally left the headlight switch in the right position, and leave it there after parking, but now the headlights stay on and drain the battery. When I turn on the headlights, the radio/clock display dims like the voltage is being pulled down. What would cause this? A stuck relay or something like that?
Thank you for any help.
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