“But I was still wondering about where the voltage reg should be set, because I’m tired of putting the charger on it.”
Set the regulator to have charging stop above 14.25 volts. The contacts should make and break slowly, not so rapidly that you see a steady arc. Adjusted for continous break/make of the regulator contact might make the lights flicker so rapidly that you don’t notice it but that mode of operation will burn up the regulator contacts pretty fast.
If the normal make and break of the regulator contacts causes an obnoxious flicker then that means that the voltage in the system is changing rapidly. Normally the battery charging and discharging will smooth things out so that the voltage change between regulator on to off won’t be fast enough to be visible.
Since you can see an abrupt brightness change look for resistance in the battery circuit ie; post, cables, ground lug etc. With the engine off and lights on, use a sensitive DVM to look for any voltage drop across what should be a solid, low resistance connection.
I’d suspect that the battery had a high internal resistance but you said you put in a new one so that’s pretty well ruled out unless the “new” battery was stored for a month or so while full of electrolyte but in a discharged state.
I looked online for an electronic voltage regulator for retrofit on your car but came up empty. If that were available it would stop the flicker too.
Good luck
This is why I recommended that he switch to an alternator that is internally regulated. External regulators are getting harder and harder to find.