While a relay harness can be a help, the Charger is different than the A-body cars in several respects.
1. Its a four lamp system.
That requires a different relay harness with more wires.
It also means that none of the lamps that can be used on out A-bodies can be used.
It takes the smaller diameter lamps, and last I looked there was no particulalry great H4 replacement for a 4002.
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2. The Charger got larger diameter 16 gage headlight wires vs the 18 gage used in the A-bodies.
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Granted its only 16 ga from the headlight switch to the dimmer, and that needs to carry current for 4 lamps when high beams are on.
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The Charger also got a 20 amps circuit breaker in its headlight switch.
Since turning off the headlights stopped the battery from charging and discharging 'wildly', the modifications don't seem to be the cause.
If the battery was supplying power to the headlamps, lets say because the alternator was failing, then when you turned the headlights off, the ammeter should have indicated charging and then returned to center.
If there was a short after the headlight switch, the circuit breaker should have opened.
Got to think about this a bit more as there may be enough clues here to point you closer. Could be something loose in the switch or in the wiring. Can't rule out hte alternator/VR and circuit yet either.
In the meantime, I would check a few things.
Battery condition. If you have a load tester or a charger, make sure the battery is fully charged. If not, measure voltage with engine off. Should be at least 12.5 Volts. Leaving the voltmeter on the battery, start the car, and see what the voltage drops to. When its running, observe the ammeter and the voltmeter.
Turn on the headlights low beam with engine off. The ammeter will show the draw from the battery. Note that and any erratic behaviour.
Turn on high beam. Does the draw increase? Is the behaviour steady or not?
Turn off lights and recharge the battery using a charger.
If any erratic behavior or high current draw is seen during the test, stop immediately.
If not too inconvenient, visually check the headlight switch connector terminals and wires. Same at the dimmer switch.
Maybe do the same behind the headlight buckets. I've seen wires chafed and rubbing where the conductors rub against each other (cross wire short) as well ground short - but those trip the breaker.
