This is the only reference to the Pendleton Mounted Infantry I could find from a Goggle search.

On further investigation, I have been unable to find a Capt. Jones or young John Breazeale in Confederate rosters..

Biographies Anderson County - South Carolina Genealogy Trails

BREAZEALE, JOHN ENOCH, lawyer, legislator, code commissioner, was born at Anderson, South Carolina, October 10, 1848.

In his boyhood and youth he worked on his father's farm, attending school for a part of each year. Although he was but sixteen, in the last year of the War between the States he served for about five months in a company of sixteen-year-old boys, stationed at Pendleton, known as the "Pendleton Mounted Infantry," W. R. Jones captain. Poor health caused him to leave the high school at Anderson in 1867, and compelled him to put aside plans he had formed for taking a college course.

http://genealogytrails.com/scar/anderson/bio__breazeale_anderson.htm