You may have a 12 v cigarette lighter-type outlet in the bathroom. You could get the 12v
from the back of it. If not, maybe from a light switch. Run a 12 ga wire which will be ample for the use, especially if you don't have to run it very far. One wire for the 12v, and then run the ground to the frame of the trailer near the water heater. It will have a ground wire in the harness. Extend it if needed to get it to a good frame attachment. Main thing is to make sure that any 12v connections you make in the wall cavities are absolutely patent and allow no possibility of shorting to the skin. The spaces are tight, so sometimes it's a challenge.