Mercedes, audi etc equip there cars with this system as standard today all around the world even in the uk. It is a proven safety feature. And soon to be standard in every new car
Mercedes, Audi etc also spend millions of dollars on research and development test labs and external testing and certification to ensure their hardware and software is reliable. What's your budget? ;)
It will only be flashing when you make an emergency brake. If normal brake the lights will work normal.
Unfortunately, That is not a supportable assertion in the real world. Nobody builds hardware failures or software errors into their products on purpose, but somehow they seem to crop up anyway (ask Toyota).
To be fair, I have no doubt that a hobbyist can make a reasonably failsafe brake light modulator without millions of dollars of R&D using an Arduino and some bits from Radio Shack. But, it does require engineering in failsafes from the get-go, serious thought to risk mitigation, and careful attention to implementation details.
For example, if it were me, I might modulate only the center brake light and let the other two remain factory. I would also arrange my circuit such that the factory circuit is uninterrupted until my modulator decides to intervene, for example through the normally closed contacts of a relay. Or if I wanted to use transistors, I'd default them to "on" with a strong pullup or pulldown resistor on the base. In the event the Arduino goes out to lunch, the lights still work as intended via the switch on the foot pedal.
I'd also wire the Arduino's digital pin through an RC time delay circuit so that software can't turn the brake lights off for more than a couple hundred ms. In case the Arduino happens to go to lunch while in the middle of an off-blink, the lights will shortly come back on and stay on as long as the foot pedal is depressed.
Don't put the Arduino between the brake pedal and the brake lights with full authority.