I had a simular problem a few years ago on my 81, battery light came on and stayed on but the car still showed NO discharge!
It took awhile, but eventually the alternator needed to be replaced. Auto Zone 30 bucks Lifetime warrantee. About 1/2 hour with basic tools. It might be worthwhile just to replace it and hope. It solved my problem maybe it will yours too.
I had the same problem a few years ago too. In my battery compartment the battery wires were frayed and shorting out, it had been rubbing up against the battery cause the battery was not tied down or anything... You may just want to check the battery wires from end to end, thats how the mechanic found mine.