The American Gothic movement sprang from the Romantic movement. The Romantic writers focused on individuals, trusting yourself, and believed that mankind was noble and ideal. It contained elements of the supernatural, had really good heroes and really evil villians, and forged the path into the individual being the focus of many stories. From this, the Gothics took a turn for the dark. They too had supernatural events, focused on the individual, and had really cool villians, but, instead of focusing on what was good and ideal in mankind, they focused on the darker side of human nature. The American Gothic movement was like the evil twin of Romanticism; it delved into insanity, crime, evil, and the dark side that each human being has buried somewhere in their souls. So, those characteristics defined the Gothic movement here in the states.
"A Rose for Emily" contains a character who definitely caves to her darker side. It tells a story of a woman who is willing to kill someone that she loves so that they won't abandon her, but, beyond this, lives in a delusional world that allows that person to still be real to her, real enough to sleep next to on a bed and pretend to cuddle. This storyline exposes the darker side of Emily's nature, reveals the "skeletons in her closet" (literally and figuratively) and makes the point that even the social elite of the old South are subject to the horrors of evil and the downfall of insecurity and immorality. It also presents a good mystery to puzzle out, and is set in a decrepit, old, decaying house and town; other elements of gothic fiction.
I hope that those thoughts help a bit; good luck!
"A Rose for Emily" illustrates several Southern Gothic traditions. The setting of Emily's old Southern home reminiscent of the antebellum South is a key element of Southern Gothic literature just as the mysterious castle is for traditional Gothic works. The house remains closed off to outsiders throughout most of the story, adding to its peculiarity.
Emily, like many Edgar Allan Poe characters, is eccentric, intimidating, and misunderstood. In addition to closing her house off from society, she also shuts herself away from the world. Also like Poe's Gothic characters, she has endured pain and loss at the hands of others and exacts revenge upon her "tormentor"--Homer Barron.
Faulkner's description of the interior of the Grierson house lends the story best to the Gothic genre. When the town leaders visit Miss Emily about taxes, Miss Emily's servant opens the long-closed blinds, and "a faint dust [rises] sluggishly about their thighs spinning with slow motes in the single sun-ray." Emily and the house are accustomed to a lack of use. Likewise, Faulkner's macabre description at the story's end of Emily's bedroom where Homer has been entombed for years surprises and shocks the reader. Poe and Hawthorne often followed this pattern for their Gothic tales.