The special folding peep seems to have been a fairly common 'cost option' as ordered originally on the pre WW2 MS.
Most of those that I have seen, however, have been installed on takedown models. My 1922 proofed M1910 takedown has it along with the removable grip cap with space for a spare sight bead (which is still present).

An entirely similar folding peep was also offered for Mausers in the 1939 Stoeger;

The full page from Westley Richards ad, 1912:

More Mannlicher Schoenauer: