Thomas Brown Hall, born 1845, served in Company K, 24th Alabama Infantry. The last servicing muster roll for his Company K is that for the period Jan/Feb, 1863. Assuming he was conscripted sometime after reaching 18 years of age,, we would not expect to see a record of his service in the records.
All of the below found in Ancestry.com Military Records
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Thomas Brown Hall, 1845-1863
http://digital.archives.alabama.gov/cdm/search/collection/voices/field/subjec/searchterm/Hall,%20Thomas%20B.%20(Thomas%20Brown),%201845-1863/mode/exact
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Poem written by Lieutenant Colonel B. F. Sawyer, honoring Thomas Brown Hall, who was mortally wounded in the Battle of Chickamauga.
http://digital.archives.alabama.gov/cdm/singleitem/collection/voices/id/4418/rec/49
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Alabama Civil War Muster Rolls, 1861-1865
Name: Thomas Hall
Military Unit: 24th Alabama Infantry Regiment
Military Unit - Company: K
Rank: Private
Place of Enlistment - State: Alabama
Roll #: 268
Archive Collection #: SG025034-11
Newspaper clipping Heroes of the War, A History of One Company from Alabama - The Company Was Organized and Equipped by Capt. B. F. Sawyer . . . .
Privates - Thomas Hall, killed at Chicamauga
Alabama Civil War Muster Rolls, 1861-1865Record Image VIEWAdd alternate informationReport issueName: Thomas HallMilitary Unit: 24th Alabama Infantry RegimentMilitary Unit - Company: KRank: PrivatePlace of Enlistment - State: AlabamaRoll #: 268Archive Collection #: SG025034-11
See also: Item #31 in pencil Hall, Thom Killed at Chickamauga
http://interactive.ancestry.com/1736/31296_195493-00024?pid=137941&backurl=http://search.ancestry.com/cgi-bin/sse.dll?gl%3D39%26gss%3Dsfs28_ms_f-39%26new%3D1%26rank%3D1%26msT%3D1%26gsfn%3DThomas%2520Brown%2520%26gsfn_x%3D0%26gsln%3DHall%26gsln_x%3D0%26msbdy%3D1845%26msddy%3D1863%26msrpn__ftp%3DAlabama%252C%2520USA%26msrpn%3D3%26msrpn_PInfo%3D5-%257C0%257C1652393%257C0%257C2%257C3246%257C3%257C0%257C0%257C0%257C0%257C%26cp%3D0%26MSAV%3D1%26uidh%3Dmfz&usePUB=true