Bouncing ammeter

It’s pretty rhythmic.
That might indicate more of a "loop" problem. FIRST thing to do is attempt to determine if you have a voltage drop problem. Tell me some more about the wiring, AKA is this factory, aftermarket, been replaced, repaired, chopped up, etc?

WHAT HAPPENS in a stock system with typical voltage drop problems:

The drop in the ignition circuit supplies the VR. This can be say, a bad connection in the bulkhead connector, the ignition switch contacts, the switch connector, etc. OR IN the output circuit in the ammeter/ bulkhead connectors part of the circuit

This can form a sort of "loop" that when the VR commands charge, the voltage comes up and the resistance in the circuit can cause a glitch in the way the VR senses. The voltage comes up, the VR starts to back back down, the voltage goes down, the VR wants more charge voltage, and it just repeats.

Things like VR grounding to battery neg, the bulkhead connectors, etc all need to be checked

Try running a BIG wire (or 2 or 3 no10 wires in parallel) direct from alternator to the battery. If that settles down the system you are on the right track.

IT IS RARE but this can also be caused by a bad VR