Hello again ...
The only things that operate solely on house power are the air conditioner, the household-style outlets, and the built-in battery charger. Those won't work unless you plug your trailer into an external source of house power. Other than those, all of the TM lights, and most of the small appliances including fans, radio, water pump, and other small appliances, operate exclusively on the battery-power system. An exception is the furnace, which uses gas to create heat, and a 12 volt fan to blow it out into the room.
Some of the appliances have the option to operate from different energy sources - you get to choose which. These include the water heater (house power or gas), and the 3-way refrigerator found in collapsible TMs (gas, house power, or battery power). I think the Elkmont refrig, being bigger, is 2-way only (gas or house power, but not battery). A quick glance at its front panel will tell you for sure.
The Forum has diagrams that outline all this, including a summary diagram at
https://www.trailmanorowners.com/for...pictureid=1969
To reflect the basic factory configuration, this diagram does not show the solar power system. If present, the solar charge controller connects directly to the + post of the battery. And for simplicity, certain battery power circuits such as the break-away switch, the propane/CO leak detector, and an electric tongue jack if you have one, are not shown.
Those are the basics. There is no need to memorize all this, as long as you are aware of the multiple systems. TM owners are a creative bunch, and have created lots of mods and upgrades to the electrical systems. These will appear in the Electrical sub-forum, and I will let you page through them at your leisure.
Bill