Charging Problems. HELP!

[ATX Custom Delux]

Truck: 1971 Chevy C10 w/ 5.7 350sb.

Timeline:
Starter failed and battery was old/low. Installed brand-new starter and battery.

Alternator removed and tested in-house at Advance Auto. Alternator Test came up GOOD. Installed all components back into truck.

Tested at O'Reilly and Auto Zone..both said battery and starter good (as they are new) but Voltage Regulator FAILED.

Purchased new external voltage regulator and installed in vehicle.

System re-tested at Advance Auto and AutoZone and AGAIN shows voltage regulator FAIL.

Current Readings via Multimeter:
Battery before start" 12.7 volts
Battery when idle: 13.6 volts
Battery with all accessories on: 12.6 volts.

Any help will be greatly appreciated as I have no idea how to proceed. Thanks in advance!