First, many thanks for Your effort to show us some "how to" hints and original tooling, which is very inspirative and clearly shows that some tasks were easier with former technology than with what we have now. Also a perfect show of KISS procedures and gadgets, which gorgeous and enginer-demanding genility build in them.
I have just heard about such a tool, sadly havenīt oportunity to inspect it myself.
Over 99,999% a rifling rod. I bet that you can see that the wood on (I suppose) the left end is broken, or thereīs evidence of sawed off/twisted off/somehow else disturbed piece of steel rod. Or maybe you can find pair of tiny holes for cross pins...
Itīs a brass-brazed tube made of sheet iron/steel. One edge of the sheet was peened or filed into wedge shape, then turned around some kind of mandrel with excess material on non-wedged side, forming a "gutter" adjacent to the tube-good for fluxing and adding the brass. Then filed off and round, but some of the brass of course remains around the seam. I bet you can find evidence of that seam, but it might be totaly covered by the brass.
Then it was (probably while hot) put on a well dried (probably also while hot) wooden stick. Way less work to form the cutter seat then. From the photo, I suppose itīs some 36-40 cal, which a bit surprises me-from what I have heard about such a design, it was used for 25-36 cal., where forminga cutter seat into steel rod is realy tricky task. Also it might be an aprenticeīs tool, which teached him how to braze precisely (wish I can do that in such a lenght...) and gave him functionable, but more forgiving option to form a cutter seat.