Are you sure he died at Vicksburg? He is not listed as being buried in the Confederate cemetery there. Although, he may have been since the original records were lost.
However, his regiment does not appear to have ever served in Vicksburg.
See the Record of Events excerpt I've copied below showing their history for the first six months of 1863.
When the regiment arrived in Mississippi, Vicksburg was under siege by Gen. Grant and reinforcements were blocked by his army from gaining entry to the city.
Record of Events for Twenty-ninth North Carolina Infantry, January 1862-December 1863.
[Webmaster's Note: Compiled Records Showing Service of Military Units, Official Records of the Confederate Armies. National Archives Microfilm Series M861, Roll #40: 29 NC Infantry.]
December 31. Took an active part in the battle of Murfreesborough in which the Twenty-ninth Regiment lost about sixty men in killed and wounded.
January 4, 1863. By order of General Bragg the Army fell back to Shelbyville at night, a distance of twenty-five miles. During the battle General Rains was killed and Colonel R. B. Vance was assigned to the command of the brigade. General McCown being relieved from duty after the battle, the division was commanded by General [Alexander Peter] Stewart during our stay at Shelbyville. Brigadier-General [William Brimage] Bate was assigned to the command of General Rains' old brigade.
May 1. Colonel R. V. Vance returned to his regiment, where he remained until he was confined by sickness and left Shelbyville. The regiment was then ordered to the Mississippi Department.
May 12-18. Left Shelbyville being detached from General Bate's Brigade and sent by order of General Bragg to Jackson, Mississippi, arriving there May l 8.
From thence we marched thirty miles to Canton. Here we took the train to Vaughan's Station on the Mississippi Central Railroad. Here the regiment was attached to a Georgia Brigade commanded by Colonel [Claudius Charles] Wilson, this brigade constituting a part of Major-General [William Henry Talbot] Walker's Division.
June l. General Walker's Division was ordered to Yazoo City and from there was ordered to Vernon, Mississippi.
June 12. General Joseph [Eggleston] Johnston, commanding the department, ordered the Nineteenth North Carolina Troops to remain and garrison Yazoo City.
July 13-27. It remained there until a division of Yankees came up Yazoo River in gunboats and compelled us to vacate the place. The regiment then marched across the county about 150 miles and joined General Johnston's Army at Morton, Mississippi. The regiment was immediately ordered by General Johnston to Meridian, Mississippi to do guard duty, etc. Arrived at Meridian by rail July 27