Mine did the same thing.
When I was restoring my car I had to get the chrome piece that holds the shift position indicator rechromed. After I removed the shift indicator I found the top of the shifter arm has a square piece that fits through the chrome trim piece ( not too technical here). That square piece is burred or hammered down to hold the trim piece in place. Over time with shifting it does not hold as well.
Two solutions: The none technical and I did this until the restoration, was to put a piece of thin cardboard between the woodgrain handle and the trim piece. This tightened it up for a while. When I restored the trim piece I simply hammered the square piece onto the chrome trim tighter. This eliminated the rattling.
