Swingarm Bearings

[Fazerider]

If you're pulling the rear wheel vertically and feeling a bit of free play it's probably the suspension linkages that are responsible rather than the swingarm pivot. Even with new bearings there, because of the large amount of leverage there is always a small bit of movement. If there is a couple of millimetres free play they are due for a change.
The play of the swingarm pivot is best checked by pulling the arm left and right or by trying to twist it while holding the top and bottom of the wheel (though you'll then need to judge if any movement is due to wheel bearings too).