Will a limited slip differential in a 1968 Mustang work while power braking?
It sounds like you have an open centre. Even with an open centre, both can spin if you have an even weight on both the rear tyres. My open centre 64 1/2 could do this too. The reason it won’t spin doubles when you apply the brakes is because one drum is likely tighter than the other. This is not an issue with a limited slip as they will constantly turn both axles at the same time. If you want to tell if you have an open centre or a limited slip, raise the rear of the car from the diff housing. Release the park brake and put the gearbox in neutral. Rotate one wheel forward, and if the other side rotates forward as well, you have a limited slip. If the other side does not rotate at all, or rotates backward, you have an open centre. Good luck.