Check out this website and read more about a James McCune's service in the Confederate Army. http://www.itd.nps.gov/cwss/soldiers.cfm
If James McCune was born in 1848, then he would have not been more than 17 when the War ended in 1865. That means he would have barely been of age. If he did indeed serve in the Army, he might have lied about his age to join sooner. That would be very unusual so late in the War.

Also, contact the Texas State Archives and see if they have files on these men for Texas State Troops.

http://www.tsl.state.tx.us/

Though the older man was not likely to be enlisted in the regular army, it is quite possible. And it would not be unusual at all for him to have served in the local homeguard, attached to Texas State Troops. From time to time, these volunteers were mustered into the Confederate Army for 6 month enlistments.

McCune, -
Confederate
Cavalry
Baird's Regiment, Texas Cavalry (Showalter's) (4th Regiment, Arizona Brigade)

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2
McCune, J. P.
Confederate
Infantry
20th Regiment, Texas Infantry (Elmore's)

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3
McCune, James
Confederate
Cavalry
4th Regiment, Texas Cavalry (4th Mounted Volunteers)

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