The speedometer needle in my 66 chevelle bounces

 

Usually this is caused by the cable needing lubrication.

 

As indicated, lack of lubrication can be a symptom of a jumpy needle. To lubricate the core, I think you are going to have to remove the cable from the instrument cluster, and then pull the core from the cable to lubricate it. I use petroleum jelly, but don't use too much, because that will cause the core to stick inside the cable, wind up and jump.

The other thing you might want to check is that all of your body grounds are making good contact. A jumpy needle can be caused by a faulty body ground and the cable is creating a false ground path.arcing internally to create a ground.