Its more complicated than a 'brisk walk'. I've spoken with T2 support regarding my apple watch and exercise minutes. It turns out that a 'brisk walk' is considered a 3.5mph pace. If you average 3.5mph for a full minute, you get a minute of credit. If you drop below 3.5mph at all in the minute, it starts over once you hit 3.5mph again and that previous minute does not count. So you legit have to be moving for 60 straight seconds. If you stop for 4 seconds, it doesn't count the minute.
Also, never carry anything in your apple watch hand. Otherwise it will most likely prevent it from reading a 3.5mph pace, even if you are going faster than that.