I saw center brake lights that also function as turn signals when deciding what to add to my Duster. I don't care for the idea, not even sure if it's legal to use.
With the regular one that is just suposed to light ( no blinky), you need to run the wire back to the brake pedal. If you just tap in to the tail circuit it will flash with the turn signals.
Yup! The cheap and nasty retrofit units that flooded the market in the '80s had so-called "logic modules" that were supposed to allow for E-Z hookup all at the back of the car. Those modules failed quicklike. Running a wire to the stop light switch is the right way to do it. Sample installation of a central stop light on a Valiant is here.