Caliper attaches to bracket. Bracket slots into swingarm. Pretty simple.

 

Hey, what exactly is moving? The entire caliper? Remember there'd be some very slight jerking movement as the back brake as it doesn't work like front which should have zero movement....THe rear caliper is floating type whereas the front is fixed. But if you can grab the rear caliper and it moves, then your mounting screws are lose. Tighten them up to specified torque values

 

 

 

 

Dude, we've all been there! Some of us (I'm looking in the mirror) more than others! I usually allot 2-3 times above what everyone else on the forums say a job will take re: time and effort. But when you get it figured out and everything comes together? Priceless...

 

ahahahahahahahahahahahahahahahahahahahahahahahahah ahahahahahahahahahahahahahahahahahahahahahahahahah ahahhahahahahahahahahaha

 

But to be fair, its only funny cause we've all done something like it before.

 

Without looking at your f4i caliper, that rear caliper design is a good one, & it looks to me that the break pads are not in their correct position giving very poor break performance & the feeling that the calipers are moving about, In short get the rear break pads pulled & correctly fit them, & unless the previous incorrect fitted break pads haven't damaged the calipers & it's mounts, you shouldn't have any dramas