Of all the Jaeger rifles shown in George Shumway's book, "JAEGER RIFLES", not one of them has a peep sight. Several of them had flip up open rear sight leaf's for shooting at longer ranges.
German target rifles did have peep sights but not their hunting rifles.
If you are not already doing this, measure the distance from your eye to the front sight on your rifle.
Then, taking your tape measure along, go to your local drug store or super market and look for some cheap reading glasses.
Measure the distance from your eye to a box on the shelf, finding something that is at a similar distance as the one you measured on your gun sight.
Pick the LOWEST power glasses they have that show the writing on the box clearly and buy them.
Wearing these glasses, shoulder your Jaeger and study the front sight. It should be fairly clear.
Now, go to a place where you can see for long distances.
Using your glasses, figure out how far you will be able to see a 6 inch diameter object clear enough to recognize it and remember the distance.
That will give you a good idea for the max range you should limit your shots to.
Happy hunting.