We had a big thread on that a few months ago, here's a good place to jump in to see some results:
Regarding center brake light flashers- I've used this one before. It has a delay feature so your chmsl isn't continuously blinking in stop-and-go traffic and driving the guy behind you crazy.
It's an old-school website, click "brake light pulser" then scroll to bottom to see universal model...
My (non-FGT) experience with electrical problems like this (where there is erratic behavior of multiple components) is that the problem is always related to a loose or corroded ground connection somewhere in the car.
Assuming the new GT radio has a conventional antenna connector, a plug-in unit will work much better than a transmitter-type unit. Still sends via an FM radio signal, but piped directly into the radio instead of through the air.
Here's one example...