Solid state regulator conversion confusion!

I don't know what you mean by a 12 gage run around wire.
The above post shows pre-70 roundbacks converted to use later regulators.
The later regulators control the field's ground rather than feed.
I wasn't trying to answer your specific question. It just happened I had accidently posted that image earlier, so it was an opportunity to show how pre-70 roundbacks are sometimes altered (mutilated).

We see an insulated brush holder and insulating washer on this alternator in the location that normally would have the grounded brush.
upload_2020-9-3_14-20-40.png

How that works with a 1970 up regulating circuit.
upload_2020-9-3_14-12-18.png

Orange arrows represent current flow. In this illustration unrestricted flow such as when the voltage at I is below the set point (probably around 13.8 V).
Functionally it doesn't really matter which brush is connected to the power and I, and which one is connected to F.
But both must be insulated from ground.