Most single seaters don't even a pit lane limiter or use the light to indicate the speed limiter (if it has one) is active.
It wasn't used in F1 because the decelerative jerk from changing gear was enough to make the light come on, and doing it on brake pressure wasn't quick enough (the cars are braking very hard before the brake pedal is pushed). It wasn't deemed good enough to use, and so it wasn't.
For the first corner caution should be your watch word. You aren't going to be threshold braking into the first corner on the first lap with lots of cars around you. It's the numpties that try to make impossible passes into the first corner that cause the accident, and having brake lights won't reduce that - they'll just wait until they see a brake light and leave it a little longer (which would probably result in the crash happening anyway).
Single seaters do not need brake lights. You know where the braking points are on the circuit, so you know, to the metre, where your opponents are going to brake. If you're behind a slower car that might be braking earlier then you don't sit behind him into a braking zone - simple.