John and Jesse Shaver were members of Co. "D", 19th Tennessee Regiment, Brig. Gen. A. P. Stewart's Brigade. Their company was recruited in Rhea County, Tenn. After the war Elmira Shaver filed for pension support from the State of Tennessee based on her husband's service with this command.
This regimental history should help with some details:
http://www.tngennet.org/civilwar/csainf/csa19.html
Do you have Confederate service records or pension applications for either of the two men mentioned?