Does this shaking occur all the time, or intermittantly ??

I can recall I car that I took out for a drivr you would cruise along and all of a sudden the steering wheel would shimy, you would bring the car to a stop, start off again go along for a short distance and the shimy would start again.

On getting the car steering box stripped down, it was found that the rubbing blocks were put on back to front, and the clearances were all up the hoooey.

So it just goes to show anything is possible