How was Homer a big part of the story?

Homer Barron's character plays a significant role in Faulkner's classic short story "A Rose for Emily." Homer Barron is a northern foreman who arrives in Jefferson to repair the sidewalks and ends up having a relationship with Miss Emily Grierson. Homer Barron's character symbolically represents northern industrial interests in the South following the Civil War, and he is viewed as a carpetbagger by the locals, who disapprove of his relationship with Miss Emily. Despite being a well-liked, popular man, the traditional citizens of Jefferson believe that Emily is making a terrible decision dating a lowly northerner who does not hail from a prestigious family. Emily continues to court Homer Barron and eventually poisons him using arsenic to prevent him from leaving her. The community takes note of Homer's absence, complains about the decaying smell coming from Miss Emily's home, and are shocked to discover Homer's skeleton in Emily's attic after she passes away. Overall, Homer's character is significant because he is Miss Emily's love interest and symbolically represents the North's industrial businesses following the Civil War. Homer Barron also emphasizes Emily's psychological issues, which further characterizes her as a traumatized, mentally-unstable woman. The extent of Emily's psychological issues is highlighted by her decision to murder the man she loved and engage in necrophilia with his body after his death.

Because Homer is only present in the town and in Miss Emily's life for a short while, it could seem that he was not a major character. That would probably have been the perspective of the townspeople. They might have thought that their disapproval had gotten through to her so she broke it off, or that he had decided to leave her.
The lapses in rational logic that seem associated with the townspeople are both necessary to the plot and to the author's overall attitude toward them. They don't investigate the odor, they don't insist she pay taxes, and they generally ignore her rather than try to help with her apparent agoraphobia. Are they polite or neglectful?
But Miss Emily was not eccentric, she was seriously ill. Homer as a real, live man would not fit into her fantasy relationship. Homer's specific attributes may not have been that important to her in that she apparently needed a symbolic husband more than a real one.