Okay, I should have noticed this particular problem sooner, but I'd honestly never driven my '65 coupe at night before!

Pull the headlight switch out one notch, dash lights come on, but nothing else, i.e. no other lights of any kind.

Pull headlights out two notches, and everything goes on, tail lights, headlamps, and the hi-beams light on the dash.

Problem with this of course is that the hi-beams aren't really meant to be running for long periods of time (Or at least I guess, something overheats.. not sure if it's the bulb, a fuse, a wire?) and so the headlamps (and dash lights, and hi-beam light) start failing intermittantly... at first just fading, then blinking randomly, then are just mostly off.

What should I be looking at first to fix this? Just the switch? Since the tailights don't go on until the hi-beams do, is it a deeper wiring issue?

Thanks for any ideas.