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i have a small weight belt (like 2-3 lbs) that goes around ankles,
Going to set one of them in the rear pouch on my seat (I have leather seats) maybe the extra weight will help dampen it, or really irriated and make it bounce more.
My guess is that you have to go within the back rest entry point for a permanent fix and mess around with some of the bolts or even add something like a shim at certain points to get it from shaking.
But if it gets to that, unless it really bothers you, don't worry about it. If you do more work other than some simple fixes like weighing it down, you might end up making it worse.
If something was rattling like that within the engine bay, then yes, worry about it a lot.