Maybe a broken piece of the old cable in the socket? Compare the old with the new as far as the length of the square end, compare the other end of the cable, you might be able to flip it inside the housing. If the square is too long, take it over to the bench grinder.

1957 Chevrolet 5700 LCF 283 SM420 2 speed rear, 1955 IH 300U T/A, 1978 Corvette 350 auto, 1978 Yamaha DT175, 1999 Harley Davidson Softail Fat Boy