Not familiar with your floorplan, but I would think you have a better chance of finding suitable supports (studs) in an exterior wall than interior. I would use a stud finder to locate them and then get a grab bar long enough to reach them on both sides. That assumes you want to mount it horizontally.
Its something I have been thinking about myself. If I go horizontal it could double as a towel rack!
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2014 Coachman Clipper 17FQ
2011 Ford Ranger 4X4
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