1992 Dodge Caravan

The headlights in this van turn themselves on randomly. After parking I can check the lights later and they will be on, even with the switch off. They stay on until the battery dies or the fuses are removed. It is only the low beams, no parking lights or any others. I started removing the fuses when the lights were not needed and a few weeks later the interior dome lights started doing it. The switch was replaced with a junkyard switch and it didn't help.
Possibly(?) Related elecrical info:
A year before this started the back wiper motor died. Soon afterwards the intermittent mode on the front wipers went away.
How do I exorcise the demons from the lights?
January 8, 2007.

Check out the related content below while we wait for the question to be answered by a professional mechanic.