[prairieschooner]

Clarke, that is what we are discussing. That is not the correct way to have the Power Inverter Installed. Actually I would recommend Source Isolation with Polarity Indication if I was to Inspect that Coach during a Survey. I would bet that if you simply unplug the Shore Cord with your Power Inverter Turned On, all of the Circuits would become Hot. The Heart Power Inverter has a Relay that Automatically Switches the Power Inverter on when the Power Source is lost, these were normally sold as Computer Back Up Systems.
I would suggest that you choose what Circuits will be Powered by the Power Inverter then correct the wiring. When I was installing Power Inverters on Yachts, I would install a Separate Panel to Power only those Circuits.
Again this is why we have this Forum, I suggest that everyone check theses older Coaches and Correct them to meet Current Standards for the Safety of our loved ones, they may be the only ones to survive. Of course this may not be the case but it only takes a few minutes to prove or disprove any potential problems.