ae82 handbrakes are always pretty shit in my experience. i've had three twin cam corolla's and only one of them has had a good hand brake. on the other two i've had you have to apply brake pressure with the pedal first then pull the hand brake up for it to work at all. I could be going along at 100km/h and pull the handbrake up and it does nothing at all.
Apparently the rear brake calipers can get damaged if you dont use the correct tools when changing the brake pads. the calipers need to be 'wound-in' rather than 'compressed-in' (the front ccalipers just need to be compressed.) if they are compressed in they fu*k up and the handbrake will no-longer work properly.
I may stnad to be corrected, but I hope this helps all the same...