The third brake light does not go through the turn signal switch. The light green wire off the brake pedal position switch and has a splice. It goes to the third brake light assembly and to the turn signal switch. Lets start with back probing the light green wire at the turn signal switch in the pin 1 position. Many times older ford pick ups the connector at the turn signal switch breaks and wires back out. There is a repair kit/connector for this issue. Ford makes it and after market also makes it. The wires tend to back out more on tilt steering columns. If we have power in and the wires/connector is good we need to see if the power is going through the switch . we can pack probe light green/orange and orange/light blue wires. These wires go the rear turn/brake lights.
lets start here
The switch might be a little different from older trucks that I have seen a lot of . I have seen a few new rangers with bad switches. Best to check with a multi meter but a test light will work.
Sometimes turning the switch left and right a few times quick will restore contacts inside and it will get the brake light to work again. I have confirmed a few this way before pulling the covers off the steering column.