My GGG-Uncle (Samuel Holly Williams, 60th Alabama, Company A) was killed at Drewry's Bluff in May of 1864. After the battle his brother, Simeon Admiral Williams (also his Captain) was granted permission to retrieve his brother's body and after obtaining permission, buired his brother in a "Private Cemetery near the battle field." This information came from a Brundidge, AL newspaper article from the 1890s.

Assuming this is all true does anyone have any idea where to start looking for this gravesite?

Thanks.