The green wire is the control wire, and the VR for a simple explanation, controls "the amount of ground" The VR controls the amount of current through the field to regulate the output voltage. The amount of current through the field causes a stronger magnetic field, and that causes more output from the alternator.
the voltage you measure on the green really does not tell you anything. I'd say you have a intermittent bad connection somewhere. "Wiggle" connections and wiring and especially the bulkhead connector.
This could be a bad regulator OR A POOR GROUND at the regulator
