Obviously putting the lights on is causing some sort of voltage drop to the coil. Is your generator light coming on? Since the CVR operates regardless of whether the lights are on or not I don't think that's your problem. The first thing I would do is put a voltmeter on the coil and check the voltage with the key on. Then see what it is with the headlights on. If there's little or no change then try it with the engine running. If it's something with the headlight switch or circuit I suspect it shouldn't matter if the engine is running or not. You should see a significant voltage drop. Before I changed out anything I would check the battery, battery cables and the ground connections to the block and firewall.