I'll bet it's a rusting or siezing U-joint. A lot of the time a joint will go tight instead of getting sloppy from wear. Take the shaft off and work the joints in all directions to find the bad one. Replace them both while it's off. There is a bushing in the tailshaft housing. If it's bad enough to cause a vibration, you should have a substantial oil leak from the tailshaft seal. Then you need a new yoke, bushing, U-joints, a seal and an O-ring or gasket to make it right. Let us know what you find,
Scott