You may have to remove the front skirt first to allow the back skirt to slide forward out of the pipes that hold the top in on the back skirt.
It’s been a while since I had one but I think that’s right.
Thats exactly how its done
Remove front unbolting 6 bolts , untwist the plastic collar on the front top , slide forward , pull rear out , pull everything back out . I removed t660 completely due to poor design and securement by paccar
To remove side fairing on og t680 first you have to remove bolts at both end at the bottom. Two at the back, and ONE up front( the one that connect that flexible thing). Then at the top back there are two very long 1/2 in bolts. Loosen them enough and push the tube from front socket.