Seems like it would be near instantaneous, right? As soon as the leader brakes, the brake lights would be on (speed of light essentially) ... the following car would recognize that, along with radar/lidar type technology. I would imagine the reaction time would be nearly instant...

Then the distance between the cars that they should hold should be calculable by enforcing braking performance on the automated cars...

Assuming its enough, a simple 2 carlength rule would 1) give enough distance to stop and 2) allow for merging easily (second car would slot into place, following cars would slow slightly to make the gap again) ...