1966 Barracuda not Charging

The diagram above shows a positive controling voltage regulator.
The voltage at the ignition terminal of the regulator determines how much current the regulator will let pass through to the alternator.
If the voltage is well below the setpoint, say 11.9 Volts, then the regulator will let as much current through as the alternator's rotor wants.

You describe using an alternator with two insulated field terminals. It can be used with a positive controlling regulator by grounding one of those terminals.
OR it can be used with a ground controlling regulator. To do so a second wire needs to be added to the system. It runs from one of the field terminals to the triangular plug on the regulator.

Knowing which setup your car has will make it easier for us to suggest the test method.