Is the head slotted to take a cleaning patch?
The only unthreaded r/rod that comes to mind is the .577 Enfield. But IIRC they are slotted and maybe shorter(?). But I'm not really up on the musket stuff.
That's my 2 drink minimum guess anyway..
I think it could be Belgian or an Afghan copy. The 1853 pattern Enfields had 39" barrels, plus the Enfield ram rods had male threads on the end for the ball puller and worm.
If you post this on the North-South Skirmish Association board, you'll probably get the answer you need. Post it in the Civil War Small Arms section.