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I have been told that limited-slip/posi was standard equipment by the late-'70s, maybe earlier, on Corvettes;
my Black Book doesn't even list it as an option...
All 81 Corvettes, as well as every other Corvette built from 1970 on came with GM's Posi-Traction. Posi became standard on Corvettes in 1970.
Federal emission 81's came with a 2.72 Posi rear axle ratio with the 4 speed and a 2.87 Posi with the automatic. With California emission equipment, both automatics and 4 speeds came with the 2.72 Posi rear axle ratio. Automatic Corvettes with California emissions could be ordered with the 2.87 ratio as a $20 "Performance Axle Ratio". Though I don't think the OP cares since this post is from 2004.
If you want to see confirmation that your car has limited slip or positraction there are two ways to do this, first jack up one wheel off the ground and try to turn it. If its posi it wont turn with the other wheel on the ground, an open differential will. The other is lift both the rear wheels off the ground and support the car either a hydraulic lift or on jackstands, now with the wheels hanging and the car in neutral, brake off turn one wheel while looking at the other. If its posi it will turn in the same direction, if its not being an open rear the other wheel will spin in the opposite direction.
This is true for early positraction, limitedslip, and suregrip rear differentials. Later model limited slip units from GM in their pickups had what’s called a gov-loc limited slip unit. If you test those like this they will act like an open rear confusing old school guys like me , they are designed to work like an open rear until one wheel slips about 5mph faster than the other then the diff locks up. They are also not as strong as the older units which earned them the nickname “gov-bomb”.
Some notes.
There is a break away test, outlined in the GM manual for testing a stock posi. Do not try this with the wheels hanging down.
If the posi was Tuned it will act like an open differential but work better than a spring loaded posi- if correctly built. Tuned posi's were never offered by GM or sold by Eaton. They are a custom built posi and usually not a problem.