1966 Barracuda not Charging

First of all stop throwing new parts at the problem.
New is not always better.

Second.
Learn to read the ammeter.
The ammeter shows how much current is flowing in or out of the battery.
This is conditional. Change the conditions and it will change.
The system voltage is also somewhat conditional. A battery that measures 12.8 Volts with no load on it may measure as low as 9 Volts when starting.
Just as important is the location of the voltage reading. Current along a path remains the same. But when current flows through resistance it loses voltage. Since you measured votlage at boththe battery and the alternator output I think you understand all that.

A battery with 11.9 Volts with no load is well below fully charged. Charge it on a charger if that's what you are reading.

As you have figured out, a slight discharge while the engine is running indicates the battery is supplying system power, therefore the alternator system is not working.
In that roundabout way the ammeter is an 'alternator gage'. But remember it does not show alternator output, just whether current is flowing in or out of the battery.

The power and charging system should looked like this.
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