This would seem to be a story in which the conflict is one of man against himself. From the very beginning Tom Benecke experiences a conflict over whether he should let the paper go or whether he should try to retrieve it.
For many seconds he believed he was going to abandon the yellow sheet, that there was nothing else to do....
But just the same, and he couldn't escape the thought, this and other independent projects, some already done and others planned for the future, would gradually mark him out from the score of other young men in his company.
He takes a long time and goes through a complex process of rationalization before he ventures out onto the narrow ledge. In fact, the author Jack Finney spends eight paragraphs describing Tom's conflicting thoughts about what to do before Tom finally puts one leg over the window-sill. One part of Tom knows all along that it is a crazy thing to be doing. If his wife had stayed at home she surely wouldn't let him climb out of an eleventh-story window and walk along a ledge that isn't even as wide as his foot.
But once he is out on the ledge he has committed himself. The internal conflict then becomes one of forcing himself to remain calm and rational against his own natural, animal fear of falling. He knows he mustn't look down. That would give the antagonist inside him, his fear and potential vertigo, the edge over the protagonist inside him, his ambition and motivation.
Tom has to fight with himself throughout this harrowing adventure. For a short while it looks as if he is going to abandon hope and let his terror win over his reason. The worst part of the experience occurs when he has to look down in order to be able to get his fingers on the yellow sheet of paper.
He saw, in that instant, the Loew's theater sign, blocks ahead past Fiftieth Street; the miles of traffic signals, all green now; the lights of cars and street lamps; countless neon signs; and the moving black dots of people. And a violent instantaneous explosion of absolute terror roared through him. For a motionless instant he saw himself externally--bent practically double, balanced on this narrow ledge, nearly half his body projecting out above the street far below--and he began to tremble violently, panic flaring through his mind and muscles, and he felt the blood rush from the surface of his skin.
So there is a back-and-forth duel between Tom Benecke and Tom Benecke. The title of the story, "Contents of the Dead Man's Pocket," leads the reader to assume that Tom is going to lose his nerve, succumb to vertigo, and fall to his death with a scream of anguish. But Tom's strength of character, augmented by his love for his beautiful wife, keep him inching his way back towards his apartment-window. He shows what Ernest Hemingway called "grace under pressure." It must be internal challenges such as this that make men climb jagged cliffs and treacherous mountains. They experience that same visceral fear but have found they can overcome it and act with their intelligence.