looks like nice old camp DR housing.
my step-down ferrule for that type of chainstay stop is just about three millimeters OD on the stepped-down portion. the ID of the ferrule end that accepts the housing is about five millimetters. i use campy non-coated housing like that on the RD of my '79 Trek with campy dropouts, or used to. now i'm using it as a short brake cable housing on a newer bike.
expensive to buy these days.
must be stainless, it never rusts.