Where is Spanish Bit?

In the wild west.

And one can more or less deduce where it would be in real life.

A narrator during the overture says Duel in the Sun happens in Texas in the 1880s. (In real history, and not the wild west, 1881 would be the most probable date.) Then the opening narration says Pearl Chavez dies at Squaw's Head Rock in Texas.

Pearl gets off the "Guadalupe coach" (from or to Guadalupe) in the town of "Paradise Flats, The Paris of the Pecos" according to the sign. There are Guadalupes in Texas, New Mexico, Arizona, Chihuahua, and Nuevo Leon, and more distant regions.

Paradise Flats is about two days' ride north of Squaw's Head Rock, and so probably over 40 miles north of the Rio Grande. On the ride to Spanish Bit that takes a few hours Jesse says his father has one million acres and the ranch is in Texas.

The Pecos River flows through western Texas to the Rio Grande.

https://en.wikipedia.org/wiki/Pecos_River

Newt rides to El Paso, Texas, and is gone for at least one day. By the maps, it might take him about a week to ride to El Paso and back if Spanish Bit was on the western edge of the Pecos River valley, and several times as long if Spanish Bit was on the eastern edge of the valley.

The Spanish Bit ranch house might be near the headwaters of Black River (or Black Creek?) about ten miles south of the New Mexico border and about seventy five miles east of El Paso.

While Newt is away, the railroad lays track up to the East Fence of the ranch and plans to lay track across the ranch. I think it would be incredibly stupid for the railroad to lay track up to the fence of a ranch without being certain that they had the right to go through the ranch.

Since the Senator opposes the railroad crossing his land, presumably some government authority has used eminent domain to seize land going through his ranch, pay him for it, and grant it to the railroad. Thus the Senator's attempts to stop the railroad by force are criminal.

In real history the Southern Pacific railroad coming east laid tracks across southern Arizona and New Mexico and reached El Paso, Texas on May 19, 1881. On December 15, 1881 their line met the Texas and Pacific Railroad at Sierra Blanca, Hudspeth County, Texas. On January 12, 1883, the Southern Pacific line met the Galveston, Harrisburg and San Antonio Railroad at a point three miles west of the Pecos River near Langtry, Texas, completing the second transcontinental railroad.

About 1881 the Texas and Pacific Railroad laying track west from Fort Worth passed north of Langtry and met the Southern Pacific track at Sierra Blanca.

https://tshaonline.org/handbook/online/articles/eqt08

It looks like the Texas and Pacific railroad was more likely to lay track west through Spanish Bit. The Texas and Pacific reached Toyah, Texas, not too far from the hypothetical location of Spanish Bit, on September 12, 1881, so I guess that the Texas and Pacific would reach Spanish Bit sometime in 1881.

http://www.ttarchive.com/Library/Articles/Texas-Pacific_Oxteams-to-Eagles.html

In the movie the railroad seems to be the fictional(?) Texas and South Western Railroad.

https://obscuretrainmovies.wordpress.com/2017/04/01/duel-in-the-sun-1946/

Jesse said the Spanish Bit ranch was (about) a million acres. An acre is 43,560 square feet, or if a square, about 208.71 by 208.71 feet. Thus if the Spanish Bit ranch was perfectly square and exactly 1,000,000 acres it would be about 208,710.32 feet by 208,710.32 feet, or about 39.528 miles by 39.528 miles.

If the Spanish Bit ranch was perfectly circular it would have a radius of about 22.30 miles and a diameter of about 44.60 miles.

Of course Spanish Bit might have a very irregular shape. The King Ranch, the real biggest ranch in Texas, has 825,000 acres, or 3,340 square kilometers, or 1,289 square miles and is so irregular that 2 of the main divisions don't connect to each other or the rest of the ranch.

https://king-ranch.com/about-us/maps/

So if Spanish Bit was near the Central Pacific line it might include land in the Mexican states of Chihuahua and/or Coahuila, while if Spanish Bit was near the Texas and Pacific Railroad it might include a lot of land in New Mexico.

When the US cavalry comes to protect the railroad workers it looks like an entire regiment, flying the regimental standards. A guidon (fork-tailed flag) says "3" above and "A" below, meaning company A of the Third United States Cavalry. The Third Cavalry was stationed in New Mexico & Arizona from 1866 to 1871, in Wyoming in 1871 to 1882, fighting in the Great Sioux War, in Arizona from 1882 to 1885, and in Texas from 1885 to 1893.

So I don't know if the 3rd Cavalry would have been in New Mexico or West Texas at the time the railroad fictionally went through the Spanish Bit ranch. But western movies aren't very accurate about which regiments were stationed where and when, or when the railroads reached various places.