[jeremyseattle]

Did you check continuity across the circuit breakers? And/or do you see a manual reset on them?

Have you tried applying 12V (or 13.7V) to the center post?

Your voltage readings obviously point to a low battery on one side - or a lot of resistantce (or partial-open?). How do the batteries read when you check them directly?

Do your voltage readings change when you start the engine and/or when on shore power? I'm guessing you're getting 13.7V on one side because you're on shore power and your converter is charging that side. Activating the solenoid should switch that, so it may just be a bad solenoid. That's why I'm curious if anything happens when you apply voltage to the control post.