I chased a gremlin in my 83' for about three weeks, had a couple of the same issues as you, charge and brake light on, good alt but no charge through the system, new reg, redid all grounds and on and on.
Gave up and put in a 94 amp GM one wire with the help of a new trail-gear chev/toy replacement alt mount. Hooked it up and all problems went away, charges great. Pulled the charge relay to end the charge and brake light problem
I hope you get yours figured out.
