Udo is right. The parallel recess would lodge whatever system in a way that it could not swing.
And the fact that, if this pistol was hanging down a belt or a bandolier by means of a hook or a ring, would cause the ramrod to easily fall off, well, such would fall off in any case, as the pistol would never be kept by whatever method with its barrel upright. The remedy for this contingency was to build the rod thick enough to get firmly stuck into the stock pipe.
I know of systems where the ramrod had a protuberance that would be caught by a little steel dent in the stock.
And back to this pistol model, allow me to be stuck up with the French influence idea. Here is a confrontation between Udo's example and the French Cavalry an IX (Full details
HERE).
... Don't tell me there are no several similarities. Probably this is about a civilian version or a contract, including variations like the hanging device ?
.