Hello fsummers,
Welcome to the forum mate, from what you describe above it does sound like it is a worm drive gearbox with a 12 volt DC motor on. This is the type you would need and usually the worm drive gearbox's have a keyed bore so you could mount it straight onto the coil winder shaft and use a torque arm to stop it spinning with the shaft. If you can put up a link to that one on ebay your post will need to be approved as your such a new member and if I see it I'll approve it straight away.
Regards Bryan