Synonyms for Vacillate:

n.

see reason/sense, reel, backpedal, move with the times, capitulate, change your mind, revise, renounce, move on. pause. repetition, teeter. decide, halt, Shilly-shally, dither. swing. vacillate (noun)
hover, oscillate, fluctuate, waver, vibrate.

v.

change (verb)
convert, set, transit, transpose, modify, change, mutate, vary, adjust, adapt, deviate, reform, transfigure, alter, fluctuate, modulate, diversify, transform.
doubt (verb)
waver, wonder, doubt, suspect, distrust, question, disbelieve.
go back and forth (verb)
hesitate, alternate, oscillate, reel, dither, stagger, hover, seesaw, sway, swing, Shilly-shally, waver, pause, fluctuate, change, rock.
oscillate (verb)
pulsate, librate, seesaw, sway, stagger, throb, wag, tremble, teeter-totter, undulate, wobble, tick, vibrate, beat, totter, radiate, bob, oscillate, rock, pulse, alternate.
procrastinate (verb)
dilly-dally, procrastinate, linger, hesitate, dawdle, filibuster, dally, stall.

Other synonyms:

Shilly-shally. teeter. pause. change
transfigure.
oscillate
librate, teeter-totter.
procrastinate
Shilly-shally.
Other relevant words:
halt, swing, hover, renounce, pause, alternate, teeter, dither, Shilly-shally, reel.