Whenever I get wobble I just slowly let off the gas and let the engine slow the bike down. I'd heard from several people that applying brake, namely the front one is just asking for disaster.
Seems like there isn't a part of the bike that can cause wobble. Seems that the head bearings are a common reason on Max's, but anything from bad/cupped tires, poor balancing, suspension setup, wheel bearings, ect can induce wobble. Tough to pinpoint exactly what might be causing it, or maybe a combo of a few things.
I did notice that wobble is more noticeable/appears at lower speeds when the tires are even a couple psi low. I usually check them at least once a week (I know, I should before every ride), and putting them back to the specified pressure usually helps.