Honestly, shimmying your steering wheel like that is not a good methodological test, if you do that with any vehicle it will still keep it straight on the road because you are moving very small increments by equal amounts on both sides. Even with a tight steering wheel shimmying it back and forth like that will likely make small movements not detectable by a shaking camera footage. I suggest you do what everyone else does, park the Jeep somewhere, roll down the window, or have someone climb under and watch the steering rack/wheels for movement.