Unless the military service record provides those answers, it's going to be necessary to look elsewhere. Tennessee pension application(s) in this name are for Willliam Anthony Cunningham of Lincoln County who served in Turney's 1st Tennessee Regiment.

There are at least thirty service files for men in Tennessee Confederate units under the name William or Wiley or W X. Cunningham, plus another half dozen or so Federal records. You could match each one of these to the 1860 census entires for men of military age by this name, and work by process of elimination. I see no other way of approaching this task.