Voltage Regulator?

The regulator reads fairly steady at 13.9V as in your test#1 with the engine running, I assume it's OK.
So in post 10 you basically use the blue ign wire currently feeding both the regulator and the ballast resistor to trigger a relay that then delivers 12V to the regulator and the ballast?

Exactly that.

On newer cars it gets worse. Some had more loads on that circuit, and later cars had an inline engine harness disconnect connector (it is white if you ever see one) and they were REAL trouble, in part because they ran the alternator output through the thing.