Geography
I have to think that "Hanging" Judge Parker's prisoner wagon was certainly going a long way in this movie.
Isaac C. Parker was the United States District Judge from 1876 to 1896 for the Western District of Arkansas which also included The Indian Territory (modern Oklahoma), with his court at Fort Smith, Arkansas. just east of the border with Indian Territory.
Fort Smith, Arkansas, is at coordinates 35°22′47″N 94°22′55″W, and the site of Fort Buchanan, Arizona, is at coordinates 31°39′27″N 110°42′25″W, 3 miles southwest of Sonoita in Santa Cruz County, Arizona. It is about 1,126.6 miles from Fort Smith to Sonoita along I-40, and over 800 miles in a straight line.
Early in the movie there is a disagreement whether to go to Dragoon Wells or to Stein's Peak. Stein's peak is in Hidalgo County, New Mexico, just across the border from Arizona, at 32°20′01″N 109°02′37″W. The man who wanted to go to Stein's Peak also said he had a shipment for Fort Bowie. The site of Fort Bowie is in Cochise County, at 32°08′46″N 109°26′08″W. So Stein's Peak is only about 25 miles in a straight line from Fort Bowie, and the character's story is rather plausible, though a lie.
The characters eventually travel though a desert to reach the fort at Dragoon Wells. The well there has been poisoned with salt. And it is said that the nearest water is at Fort Buchanan, 50 miles away.
Stein's Peak is about 103 miles in a straight line from Fort Buchanan. And the fictional fort at Dragoon Wells would be about 50 miles northeast of Fort Buchanan, probably a little west of route 191 near the tiny villages of Sunsites and Sunizona.
The problem is that if the characters meet somewhere on a line between Fort Buchanan and Stein's Peak, and closer to Stein's peak, the nearest fort would probably be Fort Bowie, and Fort Bowie is certainly operating at the fictional time of the movie, since a character said they had a shipment for Fort Bowie. Maybe Fort Bowie was temporarily abandoned at that time but was scheduled to be reoccupied soon, but not soon enough to save them from the Apaches.
I note the characters travel though mountains before reaching the flatter desert on the way to the fort at Dragoon Wells. So they probably meet somewhere on the flatter land northeast of the Chiricahua or Dos Cabeza Mountains and crossed those mountains on the way to Dragoon Wells.
I note there is a famous Dragoon Springs at 31°59′51″N 110°01′20″W near where I deduced Dragoon Wells should be.
https://en.wikipedia.org/wiki/Dragoon_Springs_Stage_Station_Site
The movie was actually filmed at Kanab, Utah; the Kanab Movie fort; the Gap, Utah; and Sedona, Arizona.
https://www.imdb.com/title/tt0050336/locations/?ref_=ttrel_sa_4