Ammeter waving when ignition is on.

they all do that from time to time
its a combination of battery on the edge of being fully charged or to put it another way voltage seen by the regulator from battery, regardless of its state of charge is bang on the switching point between charge and do not charge.

charge current comes through ammeter on standard car so you see it twitch with every on off on

The regulator is switching alternator off and on becasue it can't make up its mind what to do.

Temperature has an impact on how well a battery takes charge and to the regulator which in a modern one uses a fine balance of volatge across a small circuit to switch a power transistor off and on to provide 0-5 v into the field
it can't be half off or half on so it just flip flops
some times on the on off switch point can change with ambient temperature.

take it for a drive, get battery well charged and it will stop

problem can be made worse by the regulator not being able to see battery volatge or by being badly grounded which means it can't work out what the battery voltage is, by compariosn with ground ov
i.e loose on its mountings or they have corroded

in both cases check wires and mounting, bad connection at battery or between battery wire and the clamp can cause problems.

Dave
Thanks, this is very helpful.
The regulator is new from classic industries. It says it's electronic, instead of mechanical, so I don't know if that enters into the conclusion. I still have the previous one and I didn't think it was malfunctioning when I replaced it. I am open to the idea that the new regulator was bad or didn't work well out of the factory.
The battery was replaced recently too. I accidentally drained the previous one completely leaving the car on when I shut the engine off at the ballast resister while working on it and forgot to turn ignition off. Could that have also damaged the regulator?
The battery wires are frayed a bit at the connections. That could be something to look at. New ones are not cheap though. I can also check the connections at the regulator to make sure something didn't wiggle loose when installing.
Is a problem with the alternator causing rapid turn on/off by the regulator a possibility? I've suspected the alternator is going bad, mostly due to engine bay noise when running.
I've left it on the charger for the past few days which reads 100% now. I could test if it's alternating on and off now.