Hi there,

There's pretty much only one way the light can be on with the key off. There's a short circuit at or in the alternator between the small red exciter wire (called D+ or D61) and the large red B+ wire that runs back to the starter and on to the battery.

If the insulation in those two wires is rubbed through where it disappears around the front crank pulley, that would do it, when an alternator doesn't prove to be the trouble.

I would get the condition to occur (motor off, key off, batt light on) and carefully disconnect the exciter wire from the alt. If you have some help to watch the light for you, a wiggling might steer you right to a shorted harness if it flashes on and off, but if it goes off when you remove the connector tab, you can blame the alternator.

My drawings show a 1980 could still have an external regulator. I assume yours doesn't because you've had the alternator replaced.
--
Art Benstein near Baltimore

"Body work is just like drywall. Frame it right, hang it right, use less mud. Don't paint until its perfect." -AB