Hi Roy -
thanks for your posting; it looks like there were TWO Singletons in one of the earlier manifestations of Newton's 10th Arkansas Cavalry, Co. C. Trader's Battalion Arkansas State Cavalry, Co. C had both your ancestor Jonathan Singleton and a Read (Reed?) Singleton in it as well.
Check out the URL given below for more info if you haven't already.
ONE of these days, we will FIND Camp Reed, CSA....!!!!!!
y.o.s.,
Kenneth Byrd