1987 Chevy Suburban engine dies when headlights turn on

1987 5.7 Suburban 4x4. The truck has been running rough and cutting out the past few times I have driven it. The other day I turned on the headlights and the engine instantly died. I restarted the car with the lights off and it ran fine. When I got it home I turned on the headlights and the engine died again. I restarted and repeated the process with the same outcome, lights on; engine dies. The next day I had trouble starting the engine and suddenly the starter would not engage at all, no click. Nothing. I turned off the the vent fan, which I noticed was running and the starter would now engage. I cranked the engine a bit before it fired up but it would barely stay running and I had to keep the revs up to keep it going. I got the car to the garage and as I pulled in the garage, the engine smoothed out and it idled without any misfiring. So, I turned on the headlights and the engine kept running. I shut the car off, restarted it right back up, turned on the lights and it kept running. I shut it off, left the headlights on, resatered it and it fired right up and ran smooth as silk even as I flipped the headliths on and off repeatedly. What the heck? Any ideas?