The New York Times explains how mimicry aids persuasion, if well done.
Benedict Carey writes (excerpt):
The technique involved mirroring a person’s posture and movements, with a one- to two-second delay. If he crosses his legs, then wait two seconds and do the same, with opposite legs. If she touches her face, wait a beat or two and do that. If he drums his fingers or taps a toe, wait again and do something similar.
The idea is to be a mirror but a slow, imperfect one. Follow too closely, and most people catch it — and the game is over.
“When you’re being mimicked in a good way, it communicates a kind of pleasure, a social high you’re getting from the other person, and I suspect it activates the areas of the brain involved in sensing reward,” he said.