The continuous duty solenoid that connects the engine battery to the house battery has a pretty high failure rate in many motor homes. It is installed by the motor home manufacturer. Fleetwood is one of the few that uses a system different from most of the others but the solenoid they use also has a relatively high failure rate.
I don't know what GulfStream does for sure but for many builders the AUX solenoid is activated in one of two ways, either by the momentary AUX boost switch or by the run terminal on the ignition switch. There should be a fuse between the run terminal and the solenoid control terminal.
If you can find the solenoid you can use a multimeter to see if voltage is present on the non grounded control terminal. If voltage is there with the engine running but the solenoid doesn't close then the solenoid is probably bad.
Clay WA5NMR - Ex Snowbird - 1 year, Ex Full timer for 11 years - 2004 Winnebago Sightseer 35N Workhorse chassis. Honda Accord toad.