I swear to you, this is one solid piece, cut from a single block of wood. It does not come apart.
Since it might have been found on a desk, the first thing it suggested to me was a paperweight for two stacks of paper, side by side, like an In/Out tray. The middle piece would keep it from rolling. Unfortunately, I can’t find any reference to such a thing or even idea. It’s what I would use it for!
Yeah, but does it?
Not with that attitude it won’t!
I think the selective application of the finish is not for any functional reason, but simply because the unfinished parts are harder to get a brush into.
I suspect the finish was applied after the piece had been assembled into a larger unit. That is why I want to see the edge of the square part. That should provide some clues.
As I pointed out earlier, it looks more like the vertical piece that the spun yarn goes around, at the business end of the wheel. Since it has no wear marks, maybe it was a spare that never got used. Maybe it’s reversible (drop it into the square peg hole) to extend its life.
It’s a darning tool for gloves and mittens. Rather like this http://www.homethingspast.com/wp-content/uploads/2012/06/glove-darner-e1339086816501.jpg
I don’t think the object in the OP would be used for darning. The example you link to is narrow enough along its length that you can slip it into a sock without stretching out the sock, and offers a smooth surface on which to sew. But the object in the OP seems too broad to fit comfortably into a sock and has a pointed end that’s going to make it difficult to sew on top of.
If the acorn caps unscrew, it’s possible this might be a wooden style of nutmeg grater:
http://www.nutmeggraters.com/ivoryOrBoneNutmegGrater.html#
It might also be a double-sided pediment:http://www.architecturaldepot.com/pediments.html
Reported
Good to know that they don’t use wooden acorns in concrete coatings. While it would lead to an interesting finish, it probably would have some practical issues.