The opening words of Part II of "An Occurrence at Owl Creek Bridge" tell exactly what Peyton Farquhar's occupation was.
Peyton Farquhar was a well to do planter, of an old and highly respected Alabama family. Being a slave owner and like other slave owners a politician, he was naturally an original secessionist and ardently devoted to the Southern cause.
He owned a big tract of land which had been passed down to him by his forebears. He undoubted planted cotton and used black slaves to do all the work. There were many such plantation owners in the South, and they enjoyed prosperity because they did not have to pay for the heavy labor involved in growing, tending, and picking cotton. The cotton was baled and shipped to the textile mills in England. It was the slave owners of the South, of course, who were most strongly opposed to the growing anti-slavery movement in the north. The rich plantation owners not only thought that slavery was a benign institution but were bent on spreading it farther and farther to the west.
Peyton Farquhar's occupation was restricted to managing a big plantation. He was following in the footsteps of his ancestors who had been slave holders for generations.
When he wasn't spying for the Confederate cause, Peyton Farquar was an Alabama plantation owner. A man who appeared to be in his mid-30s, Farquar was dressed in clothing that would signify he was a "planter" and a gentleman. He had gray eyes and "long, dark hair," with a mustache and "pointed beard, but no whiskers." He had a wife and several small children back home, and they were in his thoughts as he stood awaiting his punishment. In Part II, we are told that he came from an old and "respected" family. He was a slave owner and politician (probably on the local level) who hoped to eventually become an officer and lead troops in battle. He longed for
... the larger life of the soldier, the opportunity for distinction. That opportunity, he felt, would come, as it comes to all in wartime. Meanwhile he did what he could. No service was too humble for him to perform in the aid of the South, no adventure to perilous for him to undertake...
That isn't exactly the answer I was looking for, but thanks anyway.