What role does a cigarette play in the story contents of a dead mans pocket?
To me, the purpose of the cigarette in this story is to show us in a very graphic way how little time elapses in the story.
As the story begins, Tom lights a cigarette and puts in the ashtray as Clare leaves for the movie. After Tom goes through his ordeal out on the ledge, he gets back into the apartment and finds that his cigarette is still burning. That shows he has not been out on the ledge that long.
That helps emphasize the fact that his perspective is affected by how much danger he was in. He feels like it's been a long time but his cigarette is still burning.