1996 Toyota 4Runner headlights go on spontaneously

Our 4Runner has something strange going on. The headlights will spontaneously go on even when the light switch is off. We find the battery dead and even after we jump start the car and turn the lights off with the switch, it will turn on again without us doing anything.

This happened several times last winter and early spring and then we had no problems over the spring and summer. It happened again yesterday when the weather was cold and damp for the first time in months.

The alarm in this car is finicky but it did not go off, our neighbor called to let us know she saw our lights go on. When we jump start the car, the alarm usually does go off however.

Any ideas about what could be causing this? We have not been able to have it repeat when at the repair shop and they have not heard of this happening before.