If ACC uses the brakes to slow the vehicle, it will show the brake lights. If it releases the accelerator, no brake lights show. Just like if driven normally.
If it needs to use the brakes to slow the car, it is important to warn following traffic. Not to use the brake lights would create a risk of a rear shunt.
Adaptive cruise is not there to allow the driver to relax and become distracted. It is there to help maintain steady progress, with safe following distances.
The driver particularly needs to pay attention when approaching slip roads, or when following another car and both are catching a slower vehicle. If the vehicle ahead changes lane, onto the slip, or to make an overtake, the ACC will increase speed as the radar is now 'seeing' more space. If the difference between actual speed and set speed is large, the car might accelerate quite firmly, but then moments later 'sees' the next vehicle and then brakes. In such a situation it is better for the driver to anticipate this, and use the cancel button, add speed gently to close the gap, then resume cruise to maintain speed and distance.