The dash light rheostat gets it's 12v+ supply from the round electrical plug above it, but through the printed circuit board. There are no wires. When you remove the rheostat there will be two metal pins sticking up out of the printed circuit board that the rheostat slides on to.
If the rheostat ends up being bad you can still find them, but they're stupid expensive. I've often seen people solder a wire between the two brass legs on the rheostat as a cheap fix. You won't have the ability to dim the dash lights any longer, but you'll have lights. Then again, it may just need to be taken apart and cleaned. If the spiral wound resistance wire inside of the ceramic housing has com loose then it's pretty much a hopeless case for repair. That happens often, as well.