Jumping guage & pulsing lights

You haven't answered 273's question about what type of Vreg you have. Pulsation is normal for a mechanical Vreg (60's cars) since they control the alternator field as on/off.

I am guessing the voltmeter is not factory for your car since most had an ammeter in the dash. No idea why 2 voltmeters would disagree, but as 273 says, you aren't probing the same points. As you guess, one may have more damping, but sounds like your on/off is on the order of 5 sec which is a lot of damping.

We can't do much if you don't let us know the year and model of car and all the electrical changes made to the factory design.