1975 Other Plymouth Models Engine shuts down when electrical

I have a 1975 Plymouth Scamp with the slant six.
I have a new battery, new voltage regulater, the alternator checked okay on bench test at local auto parts store.
The issue is that when I have the headlights on
and I go to turn on the heater fan, I notice a quick
dimming of the headlights, panel lights etc, only a split second. Then without warning the engine will
shut off. Now it does happen when the engine is either at idle speed and it does happen at low speed driving.
The only other thing I notice is that when the key is on in the acc position the voltage meter on the dash shows not activity, however when I turn the key to the on position prior to engaging the starter motor the quage drops quite a bit, then after the motor starts it returns to center.