If it feels like something mechanical is shifting around, check the swingarm. If it's a pre-gen, put it on the center stand, a new-gen, suspend the bike with the rear wheel off the ground. Remove the rear wheel, grab the swingarm and see if it moves laterally left to right or can be twisted. It should only pivot up and down, not move in any other direction. It could be the swingarm bushings/bearings being worn at the pivot point.
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