There was a James Gibson who served in a Polk County company and died during the war, but his age is off by ten years.

First Sergeant James Gibson enlisted in Co. D, 19th (Dawson's) Arkansas Infantry, at Rocky Comfort, Arkansas, on October 25, 1861; and was mustered into service at Nashville, Arkansas, on November 21, 1861, for twelve months. He was wounded and captured at Arkansas Post on January 11, 1863, and his right arm was amputated in a field hospital before being sent North as a prisoner of war. He was received at Gratiot Street Military Prison, St. Louis, Missouri, on January 22, 1863. The last record I have is a report that he was admitted to the prison smallpox hospital on March 12, 1863. He presumably died there, because he was not among the 19th Arkansas soldiers who were exchanged in April.

His age at enlistment in 1861 was recorded as 28 -- this may be a transcription error, because the only James Gibson who lived in Polk County when the war started was your ancestor, who would have been about 38. No other Gibson's lived in the company's recruiting area.