I checked the aperture threads from my 1937 M71 and, as close as I can measure, it came out to .218" diameter with a thread pitch of .025". That would work out to be 7/32"-40 TPI or 12-40.
mitch ol buddy. Is yours an original bolt peep???? It would look like this one I had on my '37 deluxe:
These ads clearly shows a factory bolt peep used on an early model 71:
For that matter, is this what the OP is referring to? Some here post pics of the redfield peep and call it a factory "bolt peep". Congrats to the op on buying a fine rifle too. The model 71 348 Winchester is a sweetheart of a rifle.