Alternator Issue?
 

84 Cab, 3.2 Stock
Issue is that Alternator light stays on but indicates charging.

Had a bad batter that failed test, replaced with new battery:
New Battery:
12.7 Volts

Conditions:
Key Off: Alt Light Off
Key On: (Not Started) Alt Light Off
Engine Started: Fast Idle @ 1K RPM = 13.85 volts Alt light Off
After about 1 minute Alt light comes on.
AT 2K RPM 13.85 volts Alt light remains on.
Restart Engine: 700 RPM, 12.8 volts Alt light On
@2K RPM, 13.6 volts Alt light On
Back to 700 RPM idle 13.6 volts Alt light on.

Alternator rebuilt about 2 years ago, very little usage since then.
Alt light would come on with the old / bad battery also.

Trouble shooting seems to drive me to pull the alternator out enough to check wiring connections at the back but I’ve R&R’d alternators before and it’s not that easy so wanted a sanity check before undertaking that.
Tried to follow troubleshooting instructions and previous threads but this seems to differ or I'm missing the obvious.
Is this sounding like a regulator problem?
Any easy suggestions or do I need to get the Alternator tested?
I have not tested the transmission ground strap yet, not sure of the priority of that.

did you connect the ground strap to the alt when you replaced it.
check/clean the ground from the body to the tranny.
also make sure the ground at the battery is clean

once all that is done take the car to some place like advance, they can test the alt with it on the engine.

Thanks T77911S
I'll do grounds today, Probably a couple of days before I get it out to check the Alternator. That requires a no rain verification down here in Miami.

Problem solved: 1st problem was failing diodes. Taken care of. 2nd issue was a broken wire behind cluster and that drove a very dim lighting of the bulb. Now the Battery light comes on when it's supposed to, goes out when it's supposed to and the alternator charges appropriately.
I had professional help.