I've never thought to look for markings on it, but now that I was photographing it, I see that the double-bit part (the interchangeable rod) says FELO. I looked it up. It's from Germany.
I had often admired the reinforcing ring on the wood, but hadn't examined the shaft.
My dad was a motor-pool mechanic, after the war, in Germany. He might have brought it back with him. I'm glad I have it.
The ring has a diamond (wider than high) with a U in it.