In this picture the top gun has... It would be mounted to a board, like this if you where viewing it from the top "By the cocking bar mount behind the spring" so left and right barrels really...
The top one as drawn has fired, the guns are attached to each other by the barrel mounts, they pass over the axis pin the forward one holding the return spring... So the guns move back, you pull the handle attached to the rear of the axis pin to load initally and when you let go the trigger would be depressed by a spring loaded stud which pops up out of the board after depressing to allow the lever to pass.
Then it would go BANG! The guns move back, in the board there would be cut outs inside which are studs, the studs are shown in the levers, the groves would follow the angle of the one not in the lever, and would extend forward and back respectively ie: In relation to the gun going forward from here "Try and imagine it, for now" Thus the studs operate the levers, the spring drives the guns back in so doing the empty one originally is loaded upon the rearward movement and the fired one on the forward movement.
The lower gun will then fire as per, and the process repeated opposite way round until the magazines run out.
He he, imagine it's 1886 you'd be like yee'haw