No, each corner of the car has a dedicated wire. The TS switch controls the routing, and connects the two rear ones together when centered, and connects them to the brake like switch output.
Do the both brake lights work? If so, the problem is likely right in the switch. If the right brake also does not work, it is likely the TS switch connector coming out of the column, or a fault further back in that right rear wire
If you do not have one, wander over to MyMopar and download a free service manual. Also on that site are aftermarket wiring diagrams. These are sometimes not as detailed as the service manual but are sometimes easier to follow