How is Farquhar's perception of the Sergeant significant?

Ambrose Bierce uses a lot of 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. Bierce fought in many of the war's bloodiest battles, including the Battle of Shiloh (April 1862).
One of the many specific details in the opening paragraph is that the sergeant “in civil life may have been a deputy sheriff.” This suggests that there was an acute shortage of soldiers and that a man who had any kind of government experience in civilian life would find it easy to get promoted to the highest non-commissioned rank. It suggests a shortage of soldiers because the Civil War was such a bloody affair. Approximately 620,000 Federal and Confederate soldiers died during the war.
The overall implication seems intended to suggest that all the troops, including the sergeant and captain, are not professional soldiers but civilians absorbed into the military by an agrarian nation not accustomed to having a standing army. Thus Peyton Farquhar’s “escape” seems more plausible. The officers do not know what orders to give the soldiers. The soldiers are poor marksmen.
Bierce was noted for being a bitter, pessimistic man, an agnostic, and a cynic. His story is about the dispassionate cruelty of war and the cruelty of mankind in general. The men engaged in hanging Peyton Farquhar are going about the job in a routine, mechanical fashion. They 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 sergeant might have been a deputy sheriff suggests that 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 narrator’s part, but it shows Ambrose Bierce's 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 participated in actual hangings such as the one he describes. The fact that he writes about the hanging from the point of view of the Confederate sympathizer Peyton 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 a war in which men were killing other men they had nothing against, sometimes fathers killing sons and sons killing fathers.
https://www.owleyes.org/text/occurrence-owl-creek-bridge/read/i