I think William died in Fannin Co. GA.
1860 Fannin Co. GA
Rachael Cole, b. NC, 54, widow, housekeeper
James K., b. NC, 16 farm hand
1870 Hot House, Fannin, GA
Rachel Cole, b. NC, 1802-1803
I'd lookup the Fannin County Georgia historical and genealogical societies and ask if they have a local death index, indexed newspaper death notices and cemetery inventories.
I'd ask the same questions about William to verify his death. Once you get an approximate date and place, you might be able to order a copy of his probate records. Successful Searching!