I think these have been wired in several different manners (or have been re-wired by other owners). I have a 23' Tioga that has a similar setup. However mine has a solenoid that apparently is a constant-duty model. It was wired so that pressing the button (engine off) will close the relay and releasing it will open the relay.
What I thought was odd though is that it was wired to the ignition switch so that when you start the engine the relay closes when the keyswitch gets to "on" and stays closed until you turn the engine off. So the both house and chassis batteries are always charging off the alternator when the engine is running.
I ended up replacing the button with a lighted toggle switch so I can control the process. I can manually engage it to charge the house battery off the alternator and also engage it to charge the chassis battery from the converter.
But now I don't have to load the alternator with a low house battery when starting and warming up the engine.
