good answer ygmn
I have the same, '04 Z71 3.73 rear end. Z71 or Z66 both came with the Eaton locking rear differential. At slow speed when one of your rear wheels slips it is supposed to lock up so both rear wheels turn at the same speed.
You can test it easy, all you need is a loose surface. Wet pavement, dirt road or anywhere you can break traction easy. Cut your steering wheel hard left or right then gun it from a stop, make sure nobody is in front of you ! The rear end will lock and since one rear wheel is traveling a further distance,... the rear end will get squirrly when you are turning.
Do it straight ahead too, you should be able to feel it lock.