As you no doubt know, but for others, a black powder pistol almost guaranteed it was a single action requiring thumb cocking of the hammer before shooting.
Thus Alec had to cock the hammer, point the pistol at the female cinematographer and then pull the trigger...all deliberate actions. A noose would be period appropriate.
“a black powder pistol”
Not likely.
There are reports that the gun went off unexpectedly several times before the incident. That points to a mechanical defect, likely a worn or bad sear.
In that case, a possible chain of events would include the intent to load dummy rounds into the gun, so someone looking at the gun would see bullets, making it look realistic. However a live round, which looks like a dummy round, I believe, somehow got into the cylinder.
The actor points what he believes is a “cold” gun at the camera and pulls the hammer back, a threatening move that doesn’t require pulling the trigger, so it’s not necessary that he pull the trigger on this scenario (although he may have.) The sear slips, the hammer comes down on a live round while the gun is pointed at the camera.
The reason I suspect the intent was to load the gun with dummy rounds, rather than blanks, is that special care is taken with blank loaded guns, and actors are trained not to point a blank-loaded gun at anyone. Also with the intent to creat a realistic scenario, bringing the hammer down on a dummy round does not create a realistic reaction by the actor to firing a gun.
In the event of the use of dummy rounds then the armorer or propmaster points the gun at the ground at pulls the trigger at least six times. That is standard set procedure for clearing a revolver. Another idea would be to make the casings of dummy rounds a different color so someone handling them would not mistake them for a live round. You can’t see the walls of the casings in a camera shot.