[VetteVet]

Your check on the brown wire should be with the regulator unplugged and you should get 12 volts on it and with the key on and zero with the key off. You should also get 12 volts on 3 (red wire) key on or off.

If you are not grounding the alternator to the engine block and one of the diodes has shorted, it might be grounding through the regulator ground. The regulator might not work as it should and the battery could overcharge.

I think I would take the alternator and have it checked at Autozone or wherever you do business for car parts. Make sure they put a load on it, I think there machine does that automatically when it checks output.
If it turns out the alternator is bad and you replace it, get a 12 SI internally regulated alternator for a mid 80s camaro and we'll convert you. That will solve a lot of problems.
If it is charging correctly now you could watch it and make sure the battery wasn't overcharging.