Hi Gary,
Just to follow up. I took my smoke stick apart and I couldn't find any markings that might identify it. However, on what is now the underside of the barrel, there are two dovetail notches that, at one time must have been for rear sights. On what is now the top, there are also two dove tail notches. One holds a modern style Remington adjustable sight the other is empty. The other end of the barrel has only one notch, which holds a new sight.
I think this must be an original barrel with original trigger works that must have been a farmers varmint gun, since it's only 32 caliber. I'm pretty sure the trigger mechanism is original but the brass is probably new.
Maybe I'll get an idea this weekend as what the heck I've got, based on your advise, I certainly won't be trading it for anything ordinary.
Bob