Ambrose Bierce uses many specific details in his story in order to make the incident seem vivid and real. Bierce is able to do this because he had extensive military experience during the Civil War. According to Wikipedia online encyclopedia:
At the outset of the American Civil War, Bierce enlisted in the Union Army's 9th Indiana Infantry Regiment. He participated in the Operations in Western Virginia campaign (1861), was present at the "first battle" at Philippi and received newspaper attention for his daring rescue, under fire, of a gravely wounded comrade at the Battle of Rich Mountain. In February 1862 he was commissioned First Lieutenant, and served on the staff of General William Babcock Hazen as a topographical engineer, making maps of likely battlefields.
Bierce fought at the Battle of Shiloh (April 1862), a terrifying experience that became a source for several later short stories and the memoir, "What I Saw of Shiloh".
One of many details in the opening paragraph is that the sergeant “in civil life may have been a deputy sheriff.” This suggests there was a shortage of soldiers and that a man who had had any kind of official responsibility in civilian life would find it easy to get promoted to the highest noncommissioned rank. It suggests a shortage of soldiers because the Civil War was such a bloody affair. Approximately 620,000 Federal and Confederate soldiers died.
The overall implication is that all the troops, including sergeant and captain, are not professional soldiers but civilians absorbed into the military by an agrarian nation unaccustomed to having a standing army; thus Peyton Farquhar’s “escape” seems more plausible. The officers don’t know what to tell the soldiers.The soldiers are poor marksmen.
Bierce was noted for being a bitter, pessimistic agnostic and a cynic. His story is about the dispassionate cruelty of war and of mankind in general. The men engaged in hanging Peyton Farquhar are only obeying orders. And the sergeant is in charge because he has had a little more experience in obeying orders and can be trusted to do the job correctly. The fact that the man might have been a deputy sheriff suggests he likes discipline and regimentation. He might have been an early volunteer when the war started, giving him more time to rise in the ranks.
There is no other significance in Bierce’s statement that he might have been a deputy sheriff in civil life. It is just guesswork on the anonymous narrator’s part, but it shows his shrewdness and experience. Most Civil War soldiers were farm boys and still looked and acted like farm boys when they put on their blue or gray uniforms. The sergeant probably has just a shade more of military mentality and officer quality about him, though he would never rise to being a lieutenant.
Bierce wrote a number of stories about the Civil War based on his own battlefield experience. No one who did not possess such experience could have written with such authority and in such convincing detail. Bierce must have participating in actual hangings such as he describes. The fact that he writes about the hanging from the point of view of the Confederate sympathizer Farquhar suggests that he had an ambivalent opinion about the war. He could see the justice of the Union cause and understand the feelings of the Southerners. He could appreciate the wrongness of war in which men were killing other men they had nothing against, sometimes fathers killing sons and sons killing fathers.