There are a few reasons I like the peepers. First, remember that many of mine are on tang sights. Both the Winchester type and the larger vernier sights like on my Sharps 1874's and single shots. But the same principle applies to a levergun too.
First, it typically extends the distance betweeen the front and back sights. This in turn makes for more accuracy.
Second, they are easier to find and acquire a target as the need arises.
Third, they tend to focus better for older eyes.
Fourth, it is any light, this would probably be the best sighting system I have found for quick target acquisition in low light.
Fifth, they tend to make even a poor shot like me, look better on paper.Good luck on your hunt!