over charging

Couple things.......first, many regulators are temperature sensitive or temperature compensated. So warm up the engine fully, get the battery "clear up" and "normalized" even if you have to charge it.

Battery may be old and starting to sulfate, therefore try another known good battery, or hook that one into another vehicle after checking the charge voltage of the one in there

Next make sure voltage drop is not a problem. Check voltage drop between the VR sense wire and the battery + with key "on" and engine "off." Check it again running

Check ground. with engine running "fast" check V between VR mounting flange or ground post, if separate, and battery NEG. Check again with all accessories, lights, heater, etc running

For both these tests you are hoping for a very very low reading, the lower the better. Over say, .3V or more means you have a "drop" problem.