As you can see, one wire from the stator (yellow) powers many of the lights (including headlights). From your description, you are getting an intermittent draw, dimming your headlights.
Since the headlights don't go out completely it is safe to assume that the yellow wire is intact and not grounding out. However, if the voltage regulator were leaking too much power to ground, it would cause the same issue. You stated that you replaced the regulator. In this A/C circuit the rectifier serves to dump excess power to ground, giving you 13VAC to your lights. If this fails, all the power goes to ground and can burn your coil windings in the stator.
There is also a ground screw on the stator that is subject to vibration.