Bruce,
Not knowing the whole picture, I can only give 'thoughts'. As I understand it, the 3rd brake light is tapped into both left and right brake lines, and with the help of a solid state module, will only show BRAKE even if the rear of the truck is showing a left or right turn with brakes applied. This must mean you have wires to the rear of the truck for all your tail and brake lights...right.
If all the new lights are grounded properly and have the correct wires going to them, then this 3rd light be wired incorrectly and not allowing a signal to reach the rear of the truck.
You haven't said what works and what doesn't, so I'm just flapping in the breeze. If the 3rd brake light is down stream of the flasher and turn signal flasher, and it works, there must be wires headed back to the rear that are just waiting to work too. I am headed in the wrong direction on this?
Stuart