The verb vacillate means to hesitate in choosing between different opinions or actions, being indecisive, or swaying unsteadily from one choice to the other. 

Synonyms are waffle, seesaw, waver, or fluctuate.

The word origins from Latin (1590s) vacillatus, past participle of vacillare meaning “sway to and fro, hesitate” (to and fro = move repeatedly from one place to another and back again, or from side to side). The meaning “to waver between two opinions or courses” is recorded from 1620s.

The teacher keeps on vacillating so the class was dismissed without a decision being made.

I always vacillate between studying or sleeping. 

It is not an easy decision so it is understandable why the leader vacillated.