Why?

It appears that a thick top lever was sectioned in the middle, with the peep in the middle and secured by the screw? Or maybe the screw allows the sight to be raised and lowered?
One would think having the sight at the end of the lever would be associated with an inconsistent position.
Dave posted an image of a different top lever peep here, with explanation by Clair Kofoed
https://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=116442

Kirby Hoyt at Vintage Doubles just posted this one for sale. Same idea, whatever that is. T.Page Wood with single selective trigger.

Could it simply be a means of ensuring you have properly mounted the gun? It would be interesting to try shooting it.

I was just looking at some of the other photos and the aperture is extremely large. More of a ghost ring than normal tang sight. Apparently, Kirby thinks it is for use with ball in the right barrel, but I wonder.

Nice gun if the trigger gets fixed well.

I vote ball/slug sight...best way to check would be to set up a target at 35 to 50 yards and snap a few caps with traditional ball loads (maybe even some Brenekes). I bet they would be minute of deer.

well, one of us should buy it then and find out. I nominate you, Dave.

I have seen a similar sight on a friends Alex Martin. It was a plain light game gun which makes me think not a dedicated gun for solid ball ,perhaps for large lettered shot,? LG shot for Africa/India. Or maybe an aid to ensuring a consistent mount. The fact that it folds into the top lever indicates occasional use so I suggest it could be used as a guide for the placement of large shot on dangerous game as a last resort weapon.

Not likely with this model because it’s a Westley Richards type lever. But what about a more traditional lever when wear starts in, the lever will not always center.

I think it’s for target shooting non-moving game. Maybe sitting ducks on a pond? Just a guess.

I wonder what change in point of impact would result when the sight moved with average wear ,would that be critical at 25 yards with a buckshot load ?

I think your idea of a sight for non moving game might be the answer. Used when taking deliberate aim at a sitting rabbit or wood pigeon for example , or ducks as you suggest. It would tie in with the light weight of the gun I handled and may counteract the inclination to shoot high on sitting shots.

Whatever the intended purpose it's a poor idea. It's interesting to look at, tho' I wouldn't want one.

If a man can't hit the target at shotgun range by looking down the rib that peep isn't going to help, IMO.

SRH

Perhaps it’s aim was as an aid to prevent head lifting. Many a shot is missed by not keeping your cheek on the stock. Whatever it’s intended use it didn’t catch on. Crudgington and Baker’s “The British Shotgun “ doesn’t refer to it.

Konor3inch. I agree on both points. It would be interesting to play with for a while but I don't see it as a great asset.

I think it is probably a novelty that wasn’t considered useful enough to become popular. I have looked through a few books but have had no luck in finding reference to it. I will ask a couple of gunsmiths when the Covid restrictions ease and report any insights.