The BGB has needle bearings front and rear. There should be essentially no play in the driveshaft. So that indicates a BGB repair is in the works. You have to split the tractor at the BGB to remove it. You can get parts for them on Ebay or possibly a replacement.
Here is a service manual section on the BGB. This is for a 7016, but it is the same. You can get manuals from Simplicity if you know the mfr number on your tractor