Singleton's MSG career appears to revolve around the Battle of Lexington. As best as I can tell he was Lt Col in charge of 2nd Battalion Infantry, 3rd Div under the command of Col Congrave Jackson. Gen. John B Clark was the 3rd Divisions nominal commander but was not on the ground at Lexington. Capt. James Rollins was an aide to Jackson during the battle. Major Quinton Peacher was second in command after Singleton. See: https://dl.mospace.umsystem.edu/mu/islandora/object/mu%3A367441#page/62/mode/2up
This is consistent with his statements in his plea for pardon to Rollins. It appears he joined the MSG but was not at Wilson's Creek so maybe August, was at 1st Lexington mid September and supposedly back home in November '61. He appears on a draft registration as former MSG member July 1863. Applied for his pardon early 1864. I am not sure what drove his decision to withdraw from MSG service but appears to have occurred before the general enrollment into the CSA. He was wealthy, a slave owner, well regarded in his community and had influence in 3 counties. He may have thought twice about being on campaign and decided his worth may be better protected if he stayed at home.
Rollins appears to have done much the same being elected to the US House in 1862. He pops up frequently in the Callaway/Fulton history of the war.