It could very well be a bad diode in the altenater. If you sit the altenater belt off and the problem goes away you've ruled out headlight switches, ignition system, everything except the altenater.
I agree here with the bad diode/diodes.
Do you have a voltmeter? Use the A/C scale on the low setting and check it while the engine is running. A good alternator will have no A/C voltage.