You said: "Anderson's Bible says that Benton died 09-18-1862 at Sulphur Springs. You say that Sept. 1862, the 19th left & went to Ark post. Wouldn't Benton have been mustered in sometime btwn June-Sept 1862?"
That would normally be the case. But, the situation in Arkansas and at Sulphur Springs was far from being normal during the summer of 1862. Benton, Francis and Alvin were enlisted under what was called the Conscript Act (military Draft Law) of April 1862, which was starting to be enforced in Arkansas in June of '62.
The 19th Arkansas had too many recruits because of their recruiting efforts to be a single regiment. It had 11 Companies a normal regiment had only 10 and most of the new companies had as many as 125 men in the company and a normal company was only suppose to be 75 men and officers combined. So these "extra men" were reassigned to different regiment such as the 24th Arkansas to fill out those units.
You asked; "Is there a possibility that he became ill before being mustered in?"
That is exactly what I suspect, but can not prove. In many cases at Sulphur Spring, because these men were new and did not have such things as tents and blankets other than what they may have brought from home, they were exposed to the elements and became sick from exposure. Also measles were common in the camp. If a man became sick and was sent to the hospital before he was "officially" enrolled by the enrolling officer, not the officer he enlisted under in Polk County, he would have no official record of being "mustered in" which was a formal proceeding.
You said; "Depending upon the date in Sept., Benton may have died before the 19th left Sulphur Springs."
I suspect that Benton's date of death came from Francis or Alvin. It may well have been that Benton was still in the Hospital when the 19th Ark. left about the 18th of September, and that was the last date they knew him to be alive.
You ask; Why would his records have been left with the hospital?
Many men who were in the Hospital were not assigned to a regiment until they were well enough to leave the hospital and return to duty. Since, Benton may never "officially" been "Muster In" as I explained about, he may not have had a record.
You said; Here's another question, Milley, the wife of Anderson filed for a widow's pension. Anderson died in 1871. I understand that some mother's filed on their sons who died. Were they allowed to file for a pension on a son and a husband? If that is a possibility, Milley may have filed regarding Benton as well bc he was unmarried.
Yes, mothers were allowed under the Confederate system (remembering Anderson's pension was for Union service). But again No service record, no pension. Also remember that IF the Benton Musgraves that appears in the Missouri Adjuntant Generals report, is the same Benton Musgraves of the 19th Arkansas as we suspect, they would not have been able to have cross referenced that record in the late 1800's when she applied for Benton's pension for service in Arkansas when what little records may have existed were in Missouri.
And Finally in answer to another question that you ask in another post, There have not been any records found from the Sulphur Springs Hospital or any other Hospital in the State of Arkansas even in Little Rock.