According to the information below there is a Garrett Sr. and Jr..
I would have to bet that Garrett H. Spinks is the son of Garrett Spinks.Like you I have found no proof either way, but these are the only Garrett's I can find in Ga.
1827 Clarke Co., GA
Enumerated in Capt. Davenport's Militia District. He renders 140 2nd class acres in Clarke County [no lot/district stated]; Lot 413, containing 250 3rd class acres, in the 1st District, Early County; Lot 290, containing 490 3rd class acres, originally patented to Strinchcomb, in the 1st District, Appling County; and Lot 204, containing 202.5 2nd class acres, in the 16th district, Newton, County,. In addition: he pays poll [only] for Garratt Spinks, Junr.
This is the last year that Garrett, Sr. appears on the Clarke County tax rolls. His name is not found on a defaulter list for any year. Clark County rolls were searched through 1830. Enoch Spinks is the only person by that surname enumerated on subsequent rolls. He resides in the county up to the time of his death in 1842.