The western faceoff was probably already a cliche before movies were even invented. I would be surprised if they weren’t a staple of the 19th century dime novels.
You should get some sort of prize for that one 
The walk up showdown is attributed to Wild Bill Hickok - at least according to some people who did more research than I would bother to do. It was re-enacted on that wild west history show with either Dennis Weaver or Kenny Rogers. Apparently he and the fellow with the watch didn’t like each other anyway. Bill lived, the other guy didn’t. One even more outlandish story had Wild Bill facing off against a crippled guy. So, Bill borrowed a chair, his enemy had his wheelchair, and they went at it in the middle of the street. Now that’s crazy. I have no cites so these stories may be complete bullshit, but that’s what the shows claimed.
Yup…that’s exactly what I was thinking of. That’ll teach me to trust Google with this kind of thing…
I think Bareback Mountin’ would be better. 
In an episode of South Park (Chef’s Chocolate Salty Balls), Wendy drags Stan to an independent film festival. Here’s a partial transcript. Cartman says that independent films are all about gay cowboys eating pudding, then when they go to the film festival, all the movies are about gay cowboys eating pudding.
Ah. I always miss the South Park references.
Get yourself the first six seasons on DVD. Chef’s Chocolate Salty Balls is in season three.
The original title is borderline pornographic, IMO.
The only place I’ve seen the Cowboy Showdown in the Street is in the opening credits of Gunsmoke, wherein Marshall Dillon follows up on the Cowboy Showdown in the Street with the Pained Look of Law-Enforcin’ Sorrow.