Vacillation is when you constantly change your opinion. It also refers to swinging back and forth physically.
Both meanings of vacillation involve moving back and forth in some way. The first sense is what happens when a person is wishy-washy. If you want to go to a movie, then say you don’t, then say you do after all, that’s an example of vacillation. Politicians who flip-flop are known for their vacillation because they constantly change their opinions. Also, something that is swinging or swaying in the wind is vacillating, so the movement is a vacillation.