well.... It already doesn't work.... I would experiment. I'm not recommending that though because I don't want to be liable. I've never had one apart and I doubt there will be prints online. It would be dificult to point you in the correct direction. Ohm the motor wires to check for a burned up coil. Check from one lead to the other. You want low resistance... Maybe 5 or so ohms. If you get really really high resistance, buy a new pump.

Check from each lead to the case to check for a short.
Check the operation of the knob device, I know you said rheostat, but without drawings I can't be sure. It may be a potentimeter. Check the resistance of it while turning the knob, it should change.
Let me know how you make out.