In your car the lower control arm bushings can cause vibration. They might seem perfect to the eye but as the lower arm is under spring load - you cannot test it correctly with the wheels hanging. Ideally you have to compress the spring and then lever the bushings. If they move - they are shot.
the D shaft in your car has U joints on either end, if those have wear or are bad quality or are notchy they will cause vibration. Usually shake at 60 mph is worn arm bushings or a combo of things including worn ball joints, loose wheel bearings (this model toyota requires a specific torque like old VW beetles), bad bushings etc.