Not charging with headlights on

Well I have tested the alternator as you said, with direct cable from battery to field where green cable was connect. With engine off it read the same as battery 12.78v.
Started the engine in idle the reading on the big terminal was 14.4v with engine rev up it goes up above 15v, I think it was the same on battery terminals.
I hope this means my alternator is good.

Connected the green field wire back, taking out the battery link, with engine in idle the reading on the back of alternator is 11.8v to 12.6v and very unstable.

I am going to check the wiring between regulator and alternator next.
I have Ammeter and Voltmeter and both are unstable, anything between 11 to 14v.

Appreciate any help, thank you.