Only the left and right brake lights are wired through the turn signal switch. Don't go out and buy a new turn signal switch until after you try my trick.
Does the center brake light illuminate when you depress the brake pedal? If it does, that will confirm the operation of the brake light switch at the brake pedal.
Now try this:
First get a helper to watch the lights, or park where you can see the reflection of the brake lights.
To see what you have to work with, perform the following steps:
1 - Sit in the driver's seat and turn the ignition switch to "RUN".
2 - Pull the turn signal lever part of the way back in the direction you would to operate the high beam switch.
3 - While holding the lever back operate the turn signals.
4 - If both of the signals work, smile! If the problem is the same as it was on my car, the internal positioning mechanism may be all that is damaged an there is an easy fix you can do that will cost only a dollar.
Imagine that there is a thingamabob inside the steering column that prevents the lever from moving forward. With the lever in that position, the switches remain in contact. Then imagine that the dimmer switch was pushed forward and caused the positioner to fail. Now there is a situation that allows the switches to separate and no longer make contact.
The trick is to build an external positioning device that keeps the lever from moving forward.
See how the lever extends through an opening in the steering column shroud?
Fill the gap between the turn signal lever and the forward edge of the opening in the shroud.
I found a piece of black rubber hose and:
A - Cut the hose to the same length as the forward edge of the opening in the shroud.
B - Slice the hose lengthwise.
C - Position the hose so that it fills the gap between the shroud and the lever, and secure the hose in place so that it applies rearward pressure on the lever without interfering with the necessary movements of the lever for operation of the signals and dimmer.
I hope that helps.
If you need a photo, let me know.