Right! No need to overdo it but under is even worse!
Doing the calculator thing, I get this as being around 2 amps?
That small amount of current, even double would likely not strain many of the 12VDC circuits you are likely to find. It May help to look over the fuse or breakers to see what size most of them are but I would expect not many below 10 amp?
So that opens up several things to think over. Is the battery close by so that a simgle wire could be run straight to the battery and a small fuse holder mounted inline? That would really say any "estimating" of how much more load might be added to an existing circuit. Then whetehr to run a pair of wires like lamp cord or just a single may get into where you might find metal attached to the frame, etc as a handy place to pick up ground.
OV RV DC stuff, the frame and most any metal attached to it are often used as handy grounds to let you just run one wire back to the battery.
But then if you are going to a battery that is semi-close by and easy, it can work well to just take a pair of wires for the whole and connect both hot and ground at the battery, etc.
Kind of lots of ways, run a lot more wire or shortcuts that work just as well. Lots of the decision are things like whether it has to cross the door to get there!
Part of the problem is that we don't get any real specific on drawings for the trailer group, so we have to do more hunt and peck to get the right info!
Any chance of a light in that compartment that might have 12VDC run to it and be a handy place to tie on the back side of it? We would want to verify but lots of times there is extra current available on the light circuits for the small stuff like this.