... located on outside of bathroom wall.
Jayco's schematic of that wall showed a horizontal brace at that mounting height. ... easily found with a stud finder.
It's a little higher than I first thought I would mount it, but the brace made it convenient so I used it. That turned out to be a good thing because any lower and it would be in the passageway.
A thought I had while doing this: If you didn't want to use the brace for mounting, and you had something you wanted to mount on the inside of the bathroom, you could "sandwich" them being careful not to crush the wall panels.