In "The Tell-Tale Heart," what characteristics imply the narrator's insanity regardless of his sanity claim?
I have had to assume you are referring to "The Tell-Tale Heart" as your question did not specify which of Poe's short fiction you were thinking of. Certainly it is this story where the narrator protests most vociferously to being sane where so much evidence is presented to undercut this idea. I think there is ample evidence from the very first paragraph of the story to suggest that the narrator is clearly mad:
True! - nervous - very, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses - not destroyed - not dulled them. Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad? Hearken! and observe how healthily - how calmly I can tell you the whole story.
There are a number of elements in this first paragraph that display the narrator's madness. First and foremost how the rest of the story deliberately proves that the narrator cannot tell the rest of the tale "calmly," as he himself says he can. In addition, the phrase "I heard all things in the heaven and in the earth," clearly indicates that on some level he is hallucinating - nobody can hear in such a keen manner. The fact that he hears "many things in hell" also establishes that he is perhaps diabolical in his madness, foreshadowing his grim and grisly act of murder.