From the ebay advert: "It was suggested that it might be for a 211cc New Hudson machine. I imagine the 211cc was significant, as I am now reliably informed that it is infact for a Douglas Model D from the early to mid twenties. It might suit other lightweight veteran or vintage motorcycles from about mid 1920s back."
Lesson: beware reliable informants.
It's hard to get a proper look at a New Hudson 2-speed gearbox, but in this shot you can see the oil filler projecting at the rear (in line with the two mounting studs, so it needs to go into a very particular frame) with the large square-head nut. Also the change lever at the front low down. In the VMCC register of machines there are a number of two-stroke New Hudsons with gearbox numbers 19xxx and 20xxxx, so my best guess is that the ebay gearbox 20/1596 is 1920 211cc New Hudson. Right the first time.
Cheers
Leon