Backrest spindle from a rocking chair is a good guess. The piece is 40 inches long so I'm having troubles seeing it on a chair back much less a furniture leg.
I've seen these before. This looks just like the back corner support for a late 19th early 20th century German corner shelf.
The bottom is actually the rectangular end (which blind inserted into a backing board at the base) - the top round end would have had a finial on it after it was attached to the top shelf.
Here's an example of the style of corner shelf.
Vintage Solid Wood 2 Tier Corner Shelf Floor Display Plant Stand Spindle | eBay
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The eBay example above is actually much thicker and heavier than a period piece would be but the basic design is the same.
In this period in Germany the old guild system was still the basis of industry. My wife's grandfather was a guild master woodworker pre WW I. He spoke extensively of the customs and practice of the time. There was a big movement among the craft furniture makers of the time to create lighter yet stronger pieces to show the maker's level of skill in their craft. At one time I had two of these shelves made by him during that period.
These turned parts were very popular during that period. The corner shelf design had individual risers for the two front shelf supports because the style was to make each ascending shelf a little smaller. The back support riser was the only one that ran the entire height of the corner shelf. The better made shelves of the time had two mitered hardwood boards that formed the two back "legs" below the bottom shelf. This part of the corner shelf design was added during this period because the shelves were light and easy to tip over if there wasn't a substantial base.
Interesting to note that a lot of the guild trained Germans moved to Ohio and Illinois after the first world war. Grandfather was one of them. He became a woodworker for General Electromotive in Illinois. He built cradles and shipping crates for truly giant pieces of machinery. He missed fine woodwork but was happy with the challenges of working one off designs out of tree trunk sized pieces of hardwood.
