Not sure how to rewire the brake lights to make them stay on but you could Euro switch your lights and gain the ability to have rear fog lights, which might give you some of what you are looking for.
I know the look you are trying for. My BMWz4 had rear tail lights that actually added light as you stepped on the brakes harder so people behind could tell you were not just tapping the brakes.
The Euro switch has different pins in the harness to gain different effects. I am guessing the wiring harness for the brakes will have the same sort of set up.