I don't remember a rheostat, but I do remember it was a sheet of sheet metal mounted on a frame. One of the transformer homeruns is mounted to the sheet, and the other is wired into an hand held plastic "pen" with a pointed metal end. The pattern was held on with magnets and you would use wooden rulers to make the straight lines. It more or less burned small holes in the paper...
Out of curiosity, why the interest in an old pounce machine? You can still get pounce wheels. I even have a couple in a tool box somewhere.