I'm almost sure you can just run that wire that you mentioned, between the terminals,... that will give you full brightness but it won't be adjustable. The rheostat may very well work but you need to know the number of watts it would need to handle. The rheostat is just an adjustable resistor in series with all the panel lights which works but creates a lot of heat compared to our specialized dimmer circuit. Our circuit uses transistors and a rheostat uses finely coiled resistance wire.
If I were you I'd short the contacts giving you full brightness and time to find one at a junker and maybe have it mailed to you. (you might need to disconnect the dimmer dial before you jumper it because it's dimming your other lights in a weird way).