Which hospital he died in has not been identified. However, if he died in a downtown hospital he would most likely been buried in the City Cemetery.
He died during the siege of Vicksburg, if the hospital where he died was some distance from the cemetery, he would have been initially buried near the hospital.
The 46th at the time of his death manned the siege line in the North West sector, approximately 2 miles North of the cemetery.
Following the surrender of the Vicksburg garrison, the Federals, sometime later, re-interred all those they found in the City Cemetery. A Federal Colonel compiled a list of some 3000 men so buried along with those previously interred.
This list was subsequently lost. In the 1970s a list was found with some 2000 men listed. VA Tombstones were procured and set for these men.
Later, in 1997 another list of some 77 men were found. Again, tombstones were procured.
Thus, there remains some 1000 men unaccounted for, I would assume Benjamin to be among this group. His name is not found on the Confederate Roll of Honor, Known Confederate Dead, Vicksburg Campaign, January 1852-July 1863, Gary W. Webster, "Ole Sow" Publications, 1998.
A member of the 46th did keep a journal and recorded those of his Company B who died and where buried, whether Benjamin is recorded I would not know.
See: 46th Mississippi, "Blood and Sacrifice: The Civil War Journal of a Confederate Soldier, Company B, 46th Mississippi Volunteers," by William Pitt Chambers. Edited by Richard A. Baumgartner. Roster, this 281 page 1993 issue costs around $ 22.00.