Could it be the headlights?!?

Definitely need some advice. Have a 1975 280Z. Just got it running and then moved on to the headlights (they never worked). Got them working, took the car for a spin and all seemed well. Yesterday went to go to the store and the car was dead as a doornail. Went out today and noticed the clock was working again so I fired the car up and it was running good until I turned on the headlights to see if they still worked. Not 15 seconds after the lights were turned on the car just turned itself off. It proceeded to do this twice after sitting for about 15 minutes between stalls. Could it be the wiring, alternator, voltage regulator????

HELP!!