Definition of vacillate:

part of speech: verb

To waver; to fluctuate in mind or opinion; to be unsteady or inconstant.

Usage examples:

• Elizabeth, who at once began to vacillate under the combined threats of La Mothe, the French ambassador, and the arguments of the friend of Catholics, Lord Arundel, was counter- threatened with ruin by Lord Keeper Bacon unless she would throw in her lot finally with the Protestants and continue her hostility and resistance to the Catholic Scotch party. Robert Hugh Benson in "By What Authority?".