"Pecking" order? I have noticed that within the total flock of geese there are sub flocks. Usually by breed and or who was raised with who. When a dominate flock starts toward the water pool, they start squacking as they walk. The flock that is at the pool take off quickly and the dominate flock have the pool to themselves. If any remain, they get picked on and yelled at until they leave. No harm is ever done in these encounters.
A bill thump on the back is a control thing for a goose. The ducks and chickens may not understand what it means.
When some of my goslings misbehave, I will give them a light thump on the back with the end of my fingers to mimic the geese doing so with their bills. Combined with the spoken "NO". It works about as well as telling a two year old human child no. LOL Sometimes it works, sometimes it doesn't.