Brake lights only come on when you apply the brakes, but it’s perfectly possible for your car to decelerate rapidly, perhaps in front of another vehicle, without using your right foot.
It seems to me to be a good idea for cars to be equipped with ‘brakelights’ which come on to indicate any deceleration greater than a given, statutory value. (Actually, it would be even more sensible for their brightness to be in proportion to the strength of braking, but I imagine that is a tougher technical one to deal with).
A sudden slowing might be caused by eg, engine braking or running onto a steep incline (neither of which would currently be signalled explicitly to following traffic). It would be relatively easy to wire accelerometers into the brakelights system.
This would also help alleviate one of my problems when driving behind an idiot (-might even help people driving behind me). These individuals will tailgate the vehicle in front, whilst driving in too high a gear, and then repeatedly touch the brakes. This redlight flickering is distracting and also encourages me to brake intermittently as well: a tendency which gets passed backwards in waves to other cars, causing all sorts of irritation and interruptions to the traffic flow. If these tiny touches on the brakes were screened out by the proposed system, maybe this toe tapping effect would be neutralised.