Ammeter waving when ignition is on.

I've got an electrical issue with my 1968 Barracuda. The Ammeter will drop, wave for a second, then return to normal and it does this cyclically. There is an audible click every time it drops and every time it resets. Headlights dim with the waving. It does this whenever the ignition is on or on accessories.
The gauges at the time were overreporting, going strait to full, suggesting they're getting 12v. The voltage regulator in the fuel gauge must have blew or something as soon after the fuel gauge stopped working at all and the oil and temp gauges underreported. I've had the gauges sent to be repaired and since then they all three now underreport. The ammeter has continued to do this throughout and does it with the right side dash circuit board disconnected, so it's probably not the fuel gauge.
I put in a new voltage regulator from Classic Industries several months ago. There wasn't any signs the previous one was malfunctioning and I still have it, I just replaced it anticipating problems. MD2439 - 1961-69 Mopar A & B-Body Voltage Regulator
I suspect a short somewhere but am not sure. Anyone have any leads on what's going on or how to better diagnose it?

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