I actually had a 1972 Charger SE with the hideaway headlights and a similar problem...they'd shut off, close...and then turn on and open again. Sometimes they'd do it a couple of times in a row. I had my mechanic crawling all over it looking for the problem.

He couldn't find it, so for a while I would only drive it during the day.

I actually discovered the problem when I was getting ready to change the carpet, found some crispy insulation on the wires leading to my hi/low beam pushbutton on the floor. Changed it out and the headlights began to behave themselves.

Of course, then, the problem was that they were too dim, which required me to change my alternator...