67 Barracuda Heavy Electric Load

Here are some voltage readings:
12.57 before starting and after letting the car cool off and electric radiator fan off
12.22 when I started the car and the electric fan had not kicked on yet
12.00 with the car running and the electric fan kicked on

It is back on the trickle charger now and will get another reading at the battery in an hour or two.

Yeah, that alternator isn't working.
You should be getting 13-14 volts after the motor fires up.
The alternator or the voltage regulator, one of them has given up the ghost.
(I use "cigarette lighter voltmeter," a little cheap thing for testing or monitoring.)