Cupholder-looking thing on the wall of a bathroom in a senior living condo

This thing is on the wall near the toilet in the primary suite bathroom of a condo (southeastern Connecticut, US). It looks to me like a cup holder, but the positioning relative to the toilet is all wrong for that application.

It's a senior (over 55) community, and there's other evidence that the previous occupant had mobility issues at least, so it could be something related to that.

In a possibly-unrelated plot twist, there's a weird hand-crafted wooden plug/blank on the wall almost (but not exactly) behind this thing. Bonus points for an explanation of both!