The wiring diagram for the device you're looking at appears to support only making the two rear turnsignal lamps also function as brake lights.
So if you buy that thing you still don't have a solution for making the third light act as a brake light. You'll probably need to do as someone else suggested and run a separate wire from the brake switch to operate the third light.
You could always use relays to make sure you are not exceeding load limit of the black box.
