First of all, thank you very much for the information regarding the date and place of his death. It's amazing what I've been told about him in the last few days! I wonder what the chances are of his grave having a marker with his name?
I will certainly be planning a trip to Paris, TX.
John is not one of Gideon's brothers and I'm not aware of a Bowie County. Therefore, I question if he is related.

Gideon R. Barnes is shown in family notes to have been born Jan. 16, 1832 and is the oldest of 12 children of Armstead Barnes (1809-1854) and Elizabeth Dowell (1814-1896) of near Meadville in Meade Co., KY. The brief info they had on his death was that he died in TX about Feb. 21, 1862. He had an aunt and uncle that moved to Sherman, TX in 1860 and I feel that is why Gideon was there. The uncle was Burnis B. Shacklett, a veteran of both the Mexican and the Civil War.
His brother Armstead L. (A.L.) (1845-1923) was in the 1st KY. Cav., Co. F, CSA. For a very short time he was a P.O.W. in Broadway Prison in Louisville, KY. He is buried in Star Cemetery, Harvey Co., KS with a bronze military marker. Gideon and A.L. were brothers to my 2nd great grandfather, Elijah H. There is no evidence or mention of Elijah having military service.

Can you tell me the best way to go about getting Gideon's military records? Do you think he was involved in any battles?

I regretfully do not have any further info on Gideon and do not know if he ever married. Do you need any further family information regarding his brothers and sisters, etc?