The most probable cause of the back brake sticking is the slide pin. You need to take the calipar apart and make sure the pin is not sticking. I ended up completly rebuilding the front and rear calipars of my 350X to get reliable operation.
Congratulations on owning one of the best trikes ever made.
ATCnut
82 185s - sold
83 200x (hopped up)
84 200x (stock)
84 70 (lost this one to the DMV)
85 70 (soon to have lights, a foot brake, and CDI ignition)
84 200es (parts trike) - sold
85 350X (the best)
85 350X (siezed motor, dream of a poweroll kit someday)
85 250sx (frame was trash, got parted out)
86 250sx (the tractor)
86 250sx (a nicer tractor)
86 250sx (an even nicer tractor)
87 200x (parts trike, its really rough, a dog was chewing on it for a while)
87 250es Big Red (the tank!!)