'71 Duster 340 Battery getting overcharged

OK--followed the troubleshooting steps above and got a big red flag at step 2.
1. Does not charge with VR disconnected.
2. Did exactly as described and read 12.6 volts. From 67Dart273's post it appears I have voltage drop in the path from the battery to the VR. Could this be due to a bad voltage regulator? If not, what would be my next step?
Thanks...I'm off to run errands and pick up a new VR from auto zone...might not need it, but figured it was so cheap it would be worth keeping as a spare as the one on there is so old.