"Death is a dignitary who when he comes announced is to be received with formal manifestations of respect, even by those most familiar with him." (1.2)
It is the job of soldiers to kill, and the soldiers in Bierce's story are no strangers to death. Through personification, the narrator makes death another character in the story. Though the soldiers have witnessed death numerous times, their interaction with the "dignitary" death is uniquely solemn and formal.
As Peyton Farquhar fell straight downward through the bridge he lost consciousness and was as one already dead. (3.1)
Very little separates life from death if unconsciousness is basically an identical experience. Peyton's post-hanging existence is ambiguous from the start.
Encompassed in a luminous cloud, of which he was now merely the fiery heart, without material substance, he swung through unthinkable arcs of oscillation, like a vast pendulum. Then all at once, with terrible suddenness, the light about him shot upward with the noise of a loud splash; a frightful roaring was in his ears, and all was cold and dark. (3.1)
When Farquhar awakens after being hanged, it seems as though he has already, as Hamlet would put it, shuffled off the mortal coil. Dying is often associated with darkness and light. It seems important that life is so similar to death during Farquhar's escape.
To die of hanging at the bottom of a river!—the idea seemed to him ludicrous. (3.1)
Death in Farquhar's case is not only frightening and painful, but also threatens to be somewhat amusing. Farquhar's death is doubly assured (triply, actually, since the soldiers are waiting with guns), but he still imagines the possibility of survival and escape – and that is perhaps the most ridiculous thing of all.
"To be hanged and drowned," he thought, "that is not so bad; but I do not wish to be shot. No; I will not be shot; that is not fair." (3.1)
Bierce's sardonic humor shines at its brightest in this line of dialogue. Dying of strangulation and asphyxiation is fine, but being shot is too much. In his comedic analysis of his options, Farquhar makes us wonder if there is anything fair about death.
He dug his fingers into the sand, threw it over himself in handfuls and audibly blessed it. It looked like diamonds, rubies, emeralds; he could think of nothing beautiful which it did not resemble. The trees upon the bank were giant garden plants; he noted a definite order in their arrangement, inhaled the fragrance of their blooms. A strange roseate light shone through the spaces among their trunks and the wind made in their branches the music of Aeolian harps. He had not wish to perfect his escape -- he was content to remain in that enchanting spot until retaken. (3.14)
Once Farquhar gets to dry land, his surroundings become idyllic and unfamiliar. Though he is a native of this part of Alabama, Farquhar doesn't recognize the forest. The plants, light, and music all seem to hint at a heavenly place.
As he is about to clasp her he feels a stunning blow upon the back of the neck; a blinding white light blazes all about him with a sound like the shock of a cannon -- then all is darkness and silence!
Peyton Farquhar was dead; his body, with a broken neck, swung gently from side to side beneath the timbers of the Owl Creek bridge. (3.19-20)
Despite the unknown and sometimes heavenly terrain Farquhar journeys through, all is darkness when he dies and all that remains is his corpse.