if it's not rev or gear dependent, then it has to do with your suspension or wheels/tires. When you put the car on a lift, can you move either of the front tires side to side with your hands? Seems to me like if it started suddenly, and occurs at such a low speed (relatively), it's a broken/stripped end on a tie rod/tension rod/etc. Check all the end links, and I bet you'll find it there.
If the vibration is not in the steering wheel, but with the whole car, check the same things in the rear.
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