What you have is what is known as an Eaton "corporate" rear end with the drop out center section. I believe it was referred to as a H033. It was common to 1/2 ton trucks from 55 through 62.
I don't believe there was a posi available for that unit, but if there was it would have been extremely rare.
Fred
Clutch type limited slip carrier was an option, at least in later years. Had on 30 + years ago, couldn't find clutches, etc.