How fast does your lathe go? Often needs a good deal of revs to get one to cut in, especially if it's being capricious. Close to 2K rpm isn't rare. Suggest try mains powered drill applied to drive end with dyn in vice, which should spin at 2-3000rpm, see if it cuts in with no load on, D&F together etc. If it shows loadsavolts, then hook a bulb on too. Preferably 12v, start with about 25W (car flasher bulb is good). That, if it lights and burns brightly with revs, starts to tell you a story that ought to have a happy ending. (Assuming direction of rotation is right, that is.)