Which switch do I need

[Gunner]

Everyone will know it's not a Lucas because it works.

Except in perhaps theatrical lighting circles, rheostat is a very antiquated term. The two-terminal/three-terminal thing isn't a distinguishing feature; many heavy duty lighting rheostats have three terminals for balance wiring.

Terminology aside, it sounds like a good place for a wrecking yard hunt for a switch of the right size and function. They are kind of bulky, but the ones from early Mustangs might make an adaptable item.