Midnight's Pistol is a unique gold-plated Mauser pistol.

You must have the stranger mission "The Noblest of Men, and a Woman". You get this mission from a stranger in the eastern saloon in Valentine.

Talk to the train clerk at this location in Rhodes, he will tell you that the gunslinger Billy Midnight will be on the next train. Wait outside and board the first train that arrives. Billy Midnight will be on the last train car. Follow and duel him. You can pick up Midnight's Pistol after defeating him.