I am not part of the rules team
The compendium (v0.8.0) under Pinned Down and Holy Wheel Gun they included the lines (I assume they also apply to Black Owl and other cards)
- By first casualty, this effect means the next casualty to be taken by the opposing player
after this ability is played.
- If multiple effects have been played that claim the first casualty, the player selecting that
casualty can select which applies. Once that first casualty has been chosen, any other
effects currently in play that require a dude to be selected as the first casualty are ignored.
My reading of this is that your first casualty must be chosen from the pool of "marked" dudes, but after that you are free to choose your second casualty.
So if you had Absalom, The Brute, and Clementine in a shootout with both Absalom and Brute marked as the "first casualty" you would have to choose one of those dudes first, but you could choose Clementine to be your second casualty. This does mean that even though Absalom is marked as first, since another dude is marked as first he could make it out of the shootout without being taken as a casualty.