From the History of Bates County, by W. O. Atkeson (Topeka-Cleveland: Historical Publishing Company, 1918), p. 280-281:

Pleasant Gap Township.

The topography of Pleasant Gap township is broken, mostly what is called locally, high prairie; but it is good agricultural land. It is watered principally by Double Branches and Willow creeks. Some timber is along the creeks.

History has written that those who settled in this township prior to 1839 were: the Osbornes, a large family from Illinois; two families of Requas in the southwest; Daniel Francis and two sons-in-law, Arthur and Constable; and Abram Towner, these latter being refugees from Mormon settlements in Jackson county, Missouri. Two families named Harris and Collins lived near the center of the township, Jimmy Ridge, the Walker family, and a family named Beatty. William Harvey came in 1842 from Texas and left for California in 1849. William Hagen located two miles north of the village of Pleasant Gap and went to California in '49. His brother who came at the same time, and at one time was county surveyor, left for California in 1852. Joseph Wix located, where his son now lives, in 1843. James Cockrell came some time prior to 1843, also James Cockrell, Jr. and also Larkin Cockrell and James, Jr. All went to California in '49. Henry Beaver came from Kentucky and went with the others, William Deweese and his sons, Jesse, Evan and Eliph, came from Illinois in 1844. Evan was killed in the battle of Lone Jack...

The first postoffice in the east part of the county was established in 1840, near where Pleasant Gap village now is and an old man named Anderson Cockrell was the first postmaster. A mail route was established from Boonville, Clinton, Pleasant Gap to Balltown, on the Little Osage river near where Horton now is.

This passage appears to have several errors. It treats James Cockrill Sr. and Anderson Cockrill as separate individuals (though this James Sr. is perhaps the son of Anderson's brother William), and is probably where the confusion of Anderson's name being listed as James Anderson Cockrill by family historians was derived (see Herbert J. Boothroyd's note). This may also have some connection to the curious listing for a James Cockrill, age 13 (! b. 1814), in Marriage Records of Allen County, Kentucky 1815-1865, compiled by Ona A. Willoughby (Scottsville, KY: 1938), as marrying an Elizabeth Venable, July 16, 1827.

There is also a confusion in the sentence about who went to California in 1849. It does not appear (from the census records or any other documentation, including family stories) that Larkin ever went to California with the others during the Gold Rush and it was not until 1853 when he left Missouri with the rest in the Hagen-Cockrill wagon train.

Lastly, it is some what doubtful that Henry Beaver ever resided in Kentucky, but rather he came to Missouri in the late 1840's more or less directly from Ohio.

From page 203 of the same history:

...the first school house in Pleasant Gap township was located near the Wix home. It was built of logs floored with puncheons. The school was supported by "rate bills," there being no public school fund. Neighboring townships furnished some of the pupils while others came from as great a distance as twenty miles and boarded that they might attend the school. The first was S. D. Cockrell [sic], son of the postmaster of Pleasant Gap. He was employed by the year, and for three years in successions. The school house was also used for religious purposes, the first preacher being Uncle Dicky, a good old negro from Balltown. He was a Presbyterian, and was later sent to Liberia, Africa, by the Colonization Society...

This particular history also describes West Point, Missouri which was a significant "stepping-off" place for immigrants to the West before the Civil War, though it is generally confused with Westport in modern descriptions of Oregon/California trail crossings .

Photos from Jeanne Miller's 1964 trip to Pleasant Gap, Missouri: