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Today when I parked my Z on my inclined driveway I put the gear in reverse, applied the parking brake, turned it off and took the key out, released the clutch and then released the brake pedal. But the car would roll slightly down the driveway periodically. Each time it rolled there would be a low pitch clicking sound. However the problem went away when I parked it in 1st. Also, if the car is parked on a slight incline and left in neutral, it will still roll.
Probably you didn't have the car all the way in reverse. It sounds like your parking brake wasn't locking up the rear wheels and the transmission gears were slipping by each other since they were not fully engaged. On both my 97 MN6 and my 03Z MN12 I have found I need to ensure the car is in reverse when I park it. I rarely use the parking brake since I have been the victim of parking brake malfunctions that have left me stranded. To ensure the car is all the way into reverse I push the shifter in reverse and let the clutch out just enough to engage slightly. If the gear teeth are bumping into each other instead of meshing this causes them to turn and then mesh and the shifter will move forward another half inch or so.
Aside from not having the shifter all the way in gear, you also need a parking brake adjustment. If you are capable of replacing the rotors then it is something you can do yourself, because you have to remove the rear rotors to adjust the brake shoes. What a great design! However, aside from the time it takes, it's not hard to do.
The Emergancy brake even when in pefect conditions does not work well on the vette. Personally I would not park an any incline.
I recently changed my rotors and while doing so I adjusted my parking brake shoes. If done properly the handbrake will hold the car on an incline, even without parking in gear. It's a PITA job, but it's not hard and can be done.
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