This may not be a direct answer to your query, but you may find these images to be of interest:

This peep sight, offered on new Mauser rifles advertised in the 1939 Stoeger, appears to be of the same (or very similar) type as used on Westley Richards rifles going back at least to 1912. They were also offered (via Stoeger) on new Mannlicher Schoenauer rifles and stutzen from the 1939 catalog on special order.

They are often encountered on the Take Down Model of MS (popular with the British trade). My 1922 proofed M1910 TD Model has one. Whether they were truly 'factory' installed on the MS or were installed by guild shops in the Steyr area as were scope mountings, I am unsure.

Westley Richards, 1912

Lyman 35, from 1939 Stoeger

Lyman 1A, 1939 Stoeger

Parker Hale Sportarget, 1939 Stoeger