In Edgar Allan Poe's classic short story "The Tell-Tale Heart," the old man's "vulture eye" doesn't symbolize the window of the soul of the old man whose eye it is, as might be expected, but symbolizes the window of the narrator's soul and reflects the narrator's own disturbing thoughts, emotions, and obsessions. The more the narrator fixates on the old man's "vulture eye," the more the narrator reveals about himself and his own soul.
The narrator first refers to the old man's eye descriptively, almost dispassionately, as "the eye of a vulture—a pale blue eye, with a film over it." He describes the effect that the eye has on him, that it makes his blood run cold, and "very gradually," he says, he "made up [his] mind to take the life of the old man, and thus rid [himself] of the eye forever."
Earlier in the story, the narrator assures the reader that it's only the old man's eye that vexes him and that he has no other reason for wanting to kill him.
Object there was none. Passion there was none. I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire.
Only later in the story does the narrator refer to the old man's eye as "his Evil Eye"—capitalized by Poe for effect. By calling it an "Evil Eye," the narrator personalizes and demonizes the old man's eye, portraying it as a living, malevolent force in his life that must necessarily be destroyed.
Although the narrator describes the old man's eye as "pale blue"—blue being a traditional color of evil eyes—he makes no reference to the "evil eye" in the traditional sense as the source of any curse directed towards him, or as a harbinger of death for himself or for the old man. In fact, the narrator refers to himself as "Death," the "unperceived shadow" in the old man's room.
For "seven long nights—every night just at midnight," the narrator goes to the old man's room and shines a thin ray of light from his lantern on the old man's eye. The old man's "vulture eye," his "Evil Eye," remains closed for these seven nights, but the narrator's terror of the eye and his hatred of it grow steadily over those seven nights.
On the eighth night, repeating his ritual, the narrator goes to the old man's room, but this time he shines the light from the lantern on the old man's eye, and it's open, "wide, wide open." The narrator notes that the light from the lantern shines only on the old man's eye, "but [he] could see nothing else of the old man's face or person." The narrator has disassociated himself from the old man as a person, whom he said he loved, so the narrator can focus his murderous rage solely on the seemingly disembodied "Evil Eye."
The narrator's insanity is clearly revealed when his obsession shifts from the old man's eye to the "hellish tattoo" of the old man's beating heart.
It grew quicker and quicker, and louder and louder every instant. ... And now at the dead hour of the night, amid the dreadful silence of that old house, so strange a noise as this excited me to uncontrollable terror.
The narrator almost instantly transfers his terror of the old man's evil eye to his terror of the old man's beating heart, which becomes the new focus of the narrator's rage. Once the old man is dead, his "Evil Eye" is merely an afterthought.
"His eye"—no longer "the vulture eye" or "his Evil Eye" but merely "his eye"—"would trouble me no more."