Family tree data provides the following --
Birth: 1819 - Pulaski County, Georgia.
Death: Abt 1872 - Wilcox County, Georgia.
Marriage: 22 Apr 1841 - Pulaski County, Georgia
Spouse: Bethania Louisa Butler
The 1850, 1860 and 1870 census support age for Hezekiah Atkinson, which makes him about 53 at the time of death. He would have been about 45 or 46 when enlisted at Hawkinsville in Pulaski County GA. The two sons who appear on the 1850 census might also have been in Confederate service.
According to the data George Martin provided, this man was conscripted in December 1863, which means he was eligible (or presumed to be eligible) for service under the current military law. with some exceptions, until the law of Feb 17, 1864, the Confederate government required service of able-bodied white men between the ages of 18 and 45. The law of Feb 17, 1864, placed men ages 45 to 50 in the Senior Reserves. By May 1864, Hezekiah was assigned to one of the newly-organized Georgia Senior Reserve commands.
Any man not in regular Confederate service and not disabled or otherwise exempt from militia service should have been in a "home guard" company. However, we do not know that Hezekiah was ever released from Confederate service after being conscripted in December 1863. In my opinion, a family researcher assumed the Confederate Reserves were the same as the "home guard." People make all kinds of assumptions, and this one was wrong.
Hezekiah is not on the Georgia militia census taken in February 1864. Of course he should not be found here because of his earlier conscription date for Confederate service (Dec 1863). Information on the military service records which George Martin examined match the 1860 census record, so that match is correct. Enlistment place given as Hawkinsville GA and the soldier's age in 1864 (45-46) are conclusive. Let me know if you have other questions.