"Pillar of Fire", a novelette by Ray Bradbury; first published in Planet Stories, Summer 1948, available at the Internet Archive; also at Project Gutenberg. You may have read it in one of these compilations.
A man who died in 1933 finds himself awakening in 2349 as his grave is being excavated, as all dead people are now being cremated as part of an effort to eliminate any dark or disturbing influences, including the work of Bierce, Poe, Lovecraft, etc.; the rage this generates within him at the loss of an important part of human heritage is the force which animates him as he resolves to create an army of others like him and reverse the trend.
McClure said, "At first I thought it was the finest psychosis I have ever seen. You, I mean. I thought, he's convinced himself, Lantry's convinced himself, he's quite insane, he's told himself to do all these little things." McClure talked as if in a dream, and continued talking and didn't stop.
"I said to myself, he purposely doesn't breathe through his nose. I watched your nostrils, Lantry. The little nostril hairs never once quivered in the last hour. That wasn't enough. It was a fact I filed. It wasn't enough. He breathes through his mouth, I said, on purpose. And then I gave you a cigarette and you sucked and blew, sucked and blew. None of it ever came out your nose. I told myself, well, that's all right. He doesn't inhale. Is that terrible, is that suspect? All in the mouth, all in the mouth. And then, I looked at your chest. I watched. It never moved up or down, it did nothing. He's convinced himself, I said to myself. He's convinced himself about all this. He doesn't move his chest, except slowly, when he thinks you're not looking. That's what I told myself."
The words went on in the silent room, not pausing, still in a dream. "And then I offered you a drink but you don't drink and I thought, he doesn't drink, I thought. Is that terrible? And I watched and watched you all this time. Lantry holds his breath, he's fooling himself. But now, yes, now, I understand it quite well. Now I know everything the way it is. Do you know how I know? I do not hear breathing in the room. I wait and I hear nothing. There is no beat of heart or intake of lung. The room is so silent. Nonsense, one might say, but I know. At the Incinerator I know. There is a difference. You enter a room where a man is on a bed and you know immediately whether he will look up and speak to you or whether he will not speak to you ever again. Laugh if you will, but one can tell. It is a subliminal thing. It is the whistle the dog hears when no human hears. It is the tick of a clock that has ticked so long one no longer notices. Something is in a room when a man lives in it. Something is not in the room when a man is dead in it."