Internal regulators electronics can start to fail and leak enough current internally to bootstrap the alternator into charging.
There are companies who make an internal regulator for GM or Delco Remy alternators where the replacement regulator is designed to leak enough to start the charging without a light circuit.
Perhaps your old original alternator was leaking enough current to kick itself on whereas the replacement one's regulator is not leaking current into the field winding.
I have created a charging system light using a clearance light from a trailer. If the old light and wiring is corroded or confusing take this route.
You just have to open up the clearance lamp and remove the ground connection to the mounting bolt and solder on a second wire to use in the new install.
Dave m7040
I was wondering if that might have been a possibility. I don't want to send the new alternator back if the problem is actually on my end. I did buy some bulbs and want to try to resurrect the warning light if I can this weekend. It does not take a lot of effort to swap the alternators again to see if it cures the problems. I will report back after the weekend with any progress.
I do appreciate all the comments and help!
Steve