Well , I no longer think it could be a watch winder....
The tang is similar to drill bits for a brace and bit. As if held in a "chuck". It's shape is designed to be held secure while being used. Allowing the other end of the tool /object free travel.
Use a hand crank to fit the tang instead of a chuck , and it could have been used to agitate ,or churn, or stir.
The two bumps on the edges staggered side to side and by height make me thing of fluid flow...Or cordage wrapping.
So, I've no good clue.