What shows that the narrator in The Tell-Tale Heart is insane at the time of the murder?

The narrator in "The Tell-Tale Heart" exhibits signs of insanity through his obsessive fixation on the old man's eye, which he describes as "vulture-like," leading him to justify the murder. His heightened sensitivity to sound, particularly the imagined beating of the old man's heart, reveals a fractured grasp on reality. Additionally, his erratic speech and frantic rationalizations, coupled with the complete lack of remorse after the crime, further underscore his unstable mental state. These elements collectively illustrate his descent into madness at the time of the murder.