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You can also just jack up one rear wheel with the car in neutral and the parking brake off (chock the front wheels) and then turn the wheel that's in the air. If there's a functional posi unit, the wheel won't turn. If the differential is open, the wheel will turn and the driveshaft will turn at the same time.
Note that turning a C2 Corvette's rear wheel when dangling in the air may cause problems due to binding of the axle U-joints. So be careful about that.
Probably 90% or so of Corvettes from that era had the posi option.
Tfiorino - Welcome to the Corvette Forum. You've already gotten good advice about how to determine your 65's differential ratio and whether it has posi. A lot of years have passed since these cars were new so there is a chance that someone might have changed the rear gears but if they haven't, when you look at the diff...after crawling underneath the car and looking 'up', you'll be looking for the stamped characters between the leaf spring and the strut rod bracket.
Post up what you find and to give you an idea of what you might see, check out the pic of the diff from my 65 396 Roadster. It's an FA code 3:70 posi and the date codes is after the letter codes.
Mike T - Prescott AZ
The above checks are correct unless you have a rebuilt diff with a tuned posi. If that is the case, then it will act like an open diff when checked by hand. You can do a break away test if you have the tools. The rear of the car is raised and one wheel is secured from moving. The opposite wheel is removed and a torque wrench is attached to the axle and torque checked to see how much it takes to break away or slip past the clutch spring pack. Should be 40+ ft/lb. In reality no one does this test. I suppose with all the new bore scopes on the market you could go through the fill hole and see if you get a clear picture of the posi case window or actually just to see what the case looks like since an open case is different then a posi case.