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Yes, you can reuse it. Personally, I would not.
Transmission and rearend oil is NOT contaminated like engine oil is. Engine oil is constantly contaminated by elements of combustion (mainly, small amounts which get past the rings and go down into the crankcase). Thus, if tranny and rear end parts are in good condition and metal particles are not coming off of the gears, then the oil will be suitable for reuse, especially if the mileage is minimal.
Another thing to consider. I am a strong believer in installing a magnetic drain plug in trannys and rearends so that any minute metal particles are drawn out of the oil.
Thanks for the info. I wish I had a drain in the differential, it would make the job easier. I did put a magnet in the bottom of the case the last time I had it apart.
Sorry, I forgot, you have a 62. The last year for a differential drain plug was 61 (for BOTH pass cars and Vettes). Although, there have been some VERY EARLY 62s with a drain plug.
Even though it is not correct for 62, if you wanted to add a drain plug like the 57-61 rears, this is a good way to do it. Drill/tap threads in the bottom of the housing, screw in the drain plug snugly, screw on a nut (castle nut is good) snugly, spot weld the nut in a couple of places, then drill holes in a couple of the flats on the nut (for better drainage).