Curiouser and curiouser... The one John posted from eBay doesn't have enough handle to be a mop, nor does the one I posted yesterday. Maybe the handles were lopped off for re-purposing. As a "mop twister, " it still looks on the Rube Goldberg side of things. On the other hand, one of the folks who responded on that list wrote, "Rope twister it is. Made one years ago to make rope out of surplus baling twine. A similar one is used in Nevada where I ranched to make horsehair rope. "
It looks pretty complicated for either task actually. Whichever it might be, there's gotta be a patent on the contraption, and at this point, I think that's the only way we will know for certain. Maybe they're both wrong and it's for something like pulling taffy...