What are the stock gears in the rear end of a 2 wheel drive 1996 GMC sierra 1500 extended cab/

2 wheel drive check dif numbers or 4x4 if 4x4 check dif numbers 4x4 must be the same numbers

run the fault codes
could be a problem crank/cam position sensor or bag ground wire connections

FRONT END SHIMMY AND SHAKING COULD HAVE A TIRE OUT OF BALANCELOOSE OR WORN WHEEL BEARINGS, WORN OUT BALL JOINTS,WORN OUT TIE ROD ENDS, FRONT END NEED ALIGNMENT.BRAKE ROTOR WORN OUT OR WARPED, MANY THINGS WILL CAUSE FRONT END TO SHAKE SHIMMY.

The bolts that hold everything in once out is very easy to replace. It islike removing a big turkey from the ovenwith the up most care.. The only trick is to remov the screw inside the pin holding the side gears in place which is inside the carrier housing

'99-'03 if it's the standard cab. But you'll need to look in the glove box for the options tag/sheet for the gear ratio because there are three different options: GU4=3:08 ratio, GU6=3:42, and GT4= 3:73. Pray that you don't have the GT4/3:73 because that's the hardest to find around me.

The vent valve for what?

your description sounds like the gears inside the the same differential you just replaced.

Limited slip.

i had the same issue change push button cluster

418238
If you have that much play back there, first check rear universal . If play is present in pinion with shaft removed, you will not be happy with what you find inside the cover.1/2 turn of lash in any gearset is far beyond the scope of any adjustment. Rebuilding is an exact science and must be done with special tools and lots of experience.
With any luck the u joint is bad...