Speedometer needle shaking? Check driveshaft

Have never heard of that repair. In my experience the problem has always been the speedo cable. Here is the old school way of checking the condition of the cable. Pull it from the car from the speedo end. It will have a ferule (a "stop") at the speedo end. Wipe with a rag, cleaning off any grease and dirt. Each end of cable has a square crimp in it to allow it to be "driven". Place trans end in a vise. Grab speedo end and note neutral, relaxed position. Grab tightly and try to twist cable to the left and right. If you are able to twist cable in either direction a 1/4 rotation or more, the cable is bad. Replace it. In the old days we used to make our own from bulk cable, today you will need to find a speedo shop. If the outer cable is not damaged it can be reused. Lube the cable and install. Hope this helps.