At the 12v fuse panel, where the battery wire lugs are, the battery and converter go to the same lugs (back and front), which then supply the fuses to the various 12v circuits.
OK, so you got 13.6 there which means the converter is ok on shore power. Now disconnect shore power and any 7-pin connection. You should see 12.x from battery at those lugs.
You say you got zero but you might have also disconnected the converter, don't know.
You have a battery disconnect switch somewhere, and then closer to the battery, a fuse (or DC circuit breaker) at the pos wire on the battery (might be on the neg ) to check out too.
