Reports from many who have had DW say it won't stop until you do, or almost do. The characteristic of it is a latteral oscillation of the front axle.
The JK can, though, get shaking for other reasons. I had several instances of this that I thought might be DW, but it damped out by itself after 5-10s, usually after hitting an angled expansion strip or just a bump on one side. Usually at 80+kph. Very worrying when it happens on a corner & you feel like you are going to shake off the road!
My JK had a 2" lift when I got it 2nd hand. In my case it was fixed initially by adjustable lower front control arms to adjust the caster to a better angle. I later swapped them out & installed AEV caster correction brackets. They give a smoother ride than the longer arms as the arms are again horizontal, so less shock is transferred to the body when hitting bumps. Haven't had it happen again since.