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A lot of shifting over a lot of years, or just one blown shift, can damage your manual transmission. Order a Manual Transmission Rebuild Kit and replace the parts that typically wear out or are damaged, including: front and rear main bearings, synchro rings, gaskets, seals, strut rods, springs, needle bearings, snap rings, thrust washers, and main drive nut.
Countershafts are sold separately and are recommended while you have Transmission apart. The early 1963 Corvette Borg Warner T-10, this is the kit for that transmission. The Muncie 4speed came into production around the #14,500 serial number car, or about April 1963.