An initial examination of the item shown in the picture yields nothing regarding its intended function. At a cursory glance, it resembles an unusually large plastic peg. It consists of a flat round bottom portion. There is a thin cylindrical central area. Finally, a smaller “cap” is located at the end.
While nothing about the item immediately points to its use as such, it could possibly serve as an electrically-illuminated Toilet Paper Holder. In fact, the unique configuration of the item may suggest that it fit within the interior of a toilet paper roll. The larger end may have been secured by means of a spring-loaded clamp (or similar attachment) to a bracket mounted to the wall. In addition, an electrical component contained within the plastic body of the unit likely provided a gentle glow when needed. Presumably this would occur during late evening or nighttime trips to the restroom.