When I first start my '71 (only drive it maybe once a month), the headlights pop-up despite the fact that I have not pulled out the headlight on switch. After a minute or two, if I pull the switch on, then off, the headlights will go down. Weird. Why?

You have a leak somewhere in the vacuum system that operate the headlights.  Most likely it's one or both of the headlight actuator relays by the headlights.  There's also other vacuum relays and filters in the lines but I would look at the actuator relays first.  They're widely available from vendors as reproduction parts.

Since they both go up, it is most likely something before the "T" in the hose.  My guess is a leaky hose.  Run the engine, and spray starting fluid on the hoses.  If the engine revs, go back over the hoses with the spray real slowly until you find the leak.  It is probably a good idea to replace the whole hose system if one is bad.

Larry

Thanks guys!! Something for me to do this weekend!

One other thing to look at since I had the peaka boos also when I first got my car..the wiper door..it has vacuum stuff running to it also..there is an actuator on the pass side wiper arm that can leak also..if the wiper door goes up and down when you drive check up there..I use the pinch method to find leaks since I am really scared of fire..at least a 71 is fairly simple to find schematics of where things go..look for a post from rod7515 recently..he found a link that allows you to down load the entire maual for your car..from GM..free..nice info to have..