I don't know how much they changed the 12V design in the intervening 13 years but on our previous 2006 Hurricane 34N, there was a small, black, push-button circuit breaker in a big black box about dead center at the top behind the hood. The box is partially obscured by wiring. We had to reset this breaker about every six months for some reason. It gives exactly the same problem you describe - 12V available whenever hooked to power but no 12V when disconnected.