On Parasol Pockets
These triangular pockets sewn into the sides of Lady's dresses during the 1870s and '80s are called "Parasol Pockets" and have been the subject of much debate amongst costume historians.
The debate is whether they were actually used to hold parasols or whether they were just a style of pocket at that time. There are no historical images of them actually holding parasols which does lend credence to the latter idea.
The "simply a pocket" side of the debate also points out that when ladies are shown with parasols they are always holding them.
This picture, a fashion plate from May of 1876 is a good example.
As a parasol duelling aficionado the answer is obvious to me
The fashion plates and early photos are being used to show off the outfits not the parasols. Parasols were for duelling AND for show. If the fashionable parasols which matched or complimented the outfits were to be shown then obviously they needed to be held not hidden in the pocket.
A Lady Duelist would also likely have a parasol specific for duelling and a fashionably decorated one for show. When out and about the duelling one would be carried in the pocket and the fancy one held.
Historians also point to the fact that the parasol pocket often shows up on dresses that would not likely be worn outside so why have a parasol pocket at all?
These pockets would have been used to hold the smaller Street Duelling parasols of course!
Keep your sightglass full, your firebox trimmed and your water iced.