I do not know if there is a tombstone in his name at Vicksburg, and if spelled correctly and unit ID identified. You need to contact the folks at the Vicksburg Military Park to authenticate.
I have not had the time to determine the engagement in which he died. Believe it would have been close to the siege line, North of the Jackson Road.
2nd Battalion, Alabama Light Artillery
2nd Artillery Battalion was formed at Mobile, Alabama, in Janaury, 1862, with five companies; later reduced to three. It was attached to the Department of the Gulf, and after January, 1864, the Department of Alabama, Mississippi, and East Louisiana. The unit was stationed at or near Mobile throughout the war, and participated in the conflicts at Forts Gaines and Morgan, Spanish Fort, and Fort Blakely. With 64 officers and men it surrendered on May 4, 1865. Lieutenant Colonel James H. Hallonquist was in command.
http://www.itd.nps.gov/cwss/regiments.cfm
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SECOND BATTALION OF ARTILLERY
Battery A of this battalion, under the command of Capt. Stephen
Charpentier, served in the defenses of Mobile until the spring
of 1863, when it was attached to General Featherstone's
brigade, and afterward did service in Mississippi, known as
Charpentier's battery.
Battery C served in General Hebert's brigade and lost heavily
at the siege of Vicksburg, where its captain, T. K Emanuel, was
killed. The remnant of the battery continued to serve under
the command of Capt. John D. Haynie in the army of Mobile until
the surrender.
Battery E seems to have served continuously under the command
of Capt. J. B. Hutchisson, at or near Mobile.
Source: Confederate Military History, vol. VIII, p. 311
..................
Company C, 2nd Alabama Artillery Battalion (4 guns) Capt. T. K. Emanuel served at Vicksburg in Brig. Gen. Louis Hebert's Brigade, Maj. Gen. John H. Forney"s Division
..................
Company C, 2nd Battalion Alabama Artillery
Haynie, John D, Captain, resigned December 1, 1862
Cleveland, John G. 1st Lieutenant, resigned April 12, 1862
Emanuel, Thos.K., 1st Lieut./Captain, killed at Vicksburg
Morris, James, P. 2nd Lieutenant
Sclater, John, 2nd/1st Lieut., Captain
Norman, H. T., Captain (Temporarily attached)
Company Muster Rolls
Mustered in November 1, 1861 at Mobile, Alabama
Nov 1 to Dec. 31, 1861, stationed at Camp Nelins [sp?]
Jan 1 to Feby 28, 1862, stationed at Cantonment Walter
Mar 1 to Apr 30,1862, dtd May 4, stationed at Columbus, Miss.
March 4 left Cantonment Walter and arrived at Fort Gaines Apr 26 left Fort
Gaines and arrived at Mobile Apr 29 left Mobile for Columbus. Miss.
May 1 to Jun 30,1862, stationed at Columbus, Miss.
July 1 to Aug 31,1862, stationed at Columbus, Miss.
Apr 31 to Oct 31, 1862, stationed at Camp Rogers, Miss.
Left Columbus Sept 13 to join Gen. Price. Reached Baldwyn Sept 18 and left for
Iuka on the 20th Returned to Baldwyn on the 22nd While there the company
was dismembered and portions of it assigned to Gen Mayrys Division ________
______________ were in the advance and attack on Cornith and in the retreat
there from
Oct 31 to Dec 31, 1862, temporarily serving in the Appeal Battery, stationed "On
the march to Vicksburg
The above named detachment of man are serving in the Appeal Battery
Temporarily. The balance of the Company serving in other companies. They
could not be mustered as a company I therefore mustered this detachment
that they might be paid. This muster was ordered by Gen. Hebert, Brig.Genl
Commdg.
Nov 1, 1862 to Feby 28, a detachment of Capt Haynies Co. Lt. Arty. temporairly
serving in the Appeal Battery, stationed at Snyders Mill, Miss.
Jun 30, 1863 to Feby 29,1864, Lieut. Sclaters detachment of paroled prisoners,
stationed at Cahaba
............................................
Thomas K. Emanuel, age 25, Jr. 1st Lieutenant, Capt. Haynie's Company of Light Artillery,* joined November 1, 181 at Mobile for the duration of the war, advanced to 1st Lieutenant spring of 1862, temporarily transferred to Capt. Thomas F. Tobin's Company, Tennessee Light Artillery at Baldwin, Miss.., Sept. 25, 1862, returned to duty, n.d., and promoted to Captain of his old company, killed on or about June 1, 1863 at __________, killed June 3/8, 1863 at Vicksburg
* This organization was designated at various times as Haynie's Company Light Artillery; Company C, Hallonquist's Battalion, Light Artillery,; and Company C, 2nd Battalion Alabama Light Artillery
M311: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Alabama
................
I believe he is buried in the Confederate Rest Section, Vicksburg City Cemetery, he is listed on the roll of those who died during the campaign, and reads:
Emann [sic], Thomas K, died June 4, 1863, this data originally obtained from the UDC Record, page 35 [Unit ID not identified]
[Confederate Roll of Honor, Known Confederate Dead, Vicksburg Campaign, January 1862-July 1863, Gary W. Webster, "Ole Sow" Publications, 1998]
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O. R.-- SERIES I--VOLUME XXIV/2 [S# 37], p. 329
MAY 19-JULY 4, 1863.--The Siege of Vicksburg, Miss.
No. 72.--Summary of the Casualties in the Confederate forces during the siege of Vicksburg.
OFFICERS REPORTED KILLED.
Hebert's Brigade.--Staff, Col. Charles H. Herrick; Third Louisiana, Capts. J. E. Johnson and John Kinney and Lieut. A. S. Randolph ; Twenty-first Louisiana, Capt. J. Ryan and Lieut. G. H. Mann ; Twenty-second Louisiana, Capt. F. Gomez and Lieut. R. E. Lehman; Thirty-sixth Mississippi, Maj. Alexander Yates and Capt. J. S. Tatom (Capt. T. J. Chrisman and Lieut. A. T. Murrell died of wounds); Thirty-seventh Mississippi, Lieut. J. F. H. Trussell; Thirty-eighth Mississippi, Capt. L. M. Graves and Lieut. H. Lanehart (Capt. W. A. Selph died of wounds); Forty-third Mississippi, Lieut. M.D. L. Hodo; Seventh Mississippi Battalion, Capt. S.C. Pearson and Lieut. J. C. C. Welborn (Capt. W. T. Baylis died of wounds); Appeal Battery, Capt. W. N. Hogg and Lieut. R.S. Walker; Emanuel's battery, Capt. T. K. Emanuel; Pointe Coupee Artillery, Lieut. O. D'Antigue.
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For other information,
http://history-sites.com/%7Ekjones/alarty.html#2nd-Arty