I want to weigh in here, because I have
successfully kept an auxiliary "camping" battery charged in my pickup's camper shell by a method that should transfer to Teardrops without any problem. Some folks have described this system above, but no circuit diagrams.
I wanted to keep a jumpstart/air compressor/12V supply charged in the back of the truck so it would be ready to use, if I needed it in the Boonies. Even if I only wanted to use the camper shell's dome light without draining the truck's battery. Or charge my phone. Or other small uses. It's a small battery, compared to a regular car/truck battery.
First consideration was that I expected the truck's charging system would not properly charge the jumpstart battery directly. Also, I did not want all the grief and short battery life that goes with paralleling dissimilar batteries.
Second, I wanted the shell system to be independent of the rest of the truck when the engine is turned off. I also wanted to be able to listen to the truck radio while sitting there with the engine off without any drain from in back.
Third, I didn't want to have to remember to flip a switch or do any other form of "operating."
But! The jumpstart has it's own built-in charger, which I assume is tailored to the battery's needs. It just needs a little bit of 110VAC.
The plan was to power a 12VDC inverter to supply the jumpstart with 110VAC. Without having to worry about remembering to turn the system on or off. All it has to do is just work.
The circuit diagram below shows how I did it. All it takes is 2 automotive relays, a couple of inline fuses, some crimp connectors, and someplace to mount the components. One relay and fuse goes in the tow vehicle and one each goes in the trailer. I wouldn't use less than 10 gauge wire coming off the TV battery. 8 gauge might be better for voltage drop. The "hot when running" wire can be 16 or 18 gauge, as it only has to carry a little current a short distance. Pick a good battery charger for the trailer, like one of those 3-stage ones.
To find the "hot when the TV is running" wire you will also need one of these: a wiring diagram for your tow vehicle, or a 12 volt test light, or a voltmeter, or your favorite mechanic if you are scared of electricity or technical stuff. WARNING: I
strongly advise you to use a "hot when running" circuit that
doesn't supply the engine computer, ignition system, fuel injectors or transmission. I did on the first try and got weird, annoying results. A power window circuit works really good. You are only powering a relay from this circuit, so it doesn't need to be heavy duty.
I've been running this system for about 3 years without any problems, and the jumpstart battery shows a full charge every time I use the built-in tester. The only problem I encountered was my original choice for the "hot when running" circuit was a bad one. I got check engine lights and funny transmission shifting. See the warnings in the paragraph above. When I switched to the power window circuit, the weirdness went away, and I was a happy camper.
Anyway, this worked so well that I will be using this approach in my soon-to-begin build. Another relay could add the feature of automatically running the charger from shore power when connected.