I'm inclined to believe Thomas M. Hall, son of William G. and Mary Hall, of Lauderdale County was the soldier in this unit.
Name: William G Hall
Age: 39
Estimated birth year: abt 1811
Birth Place: Tennessee
Gender: Male
Home in 1850: Southern District, Lauderdale County, Mississippi
Household Members: Name / Age
William G Hall 39
Mary Hall 38
Darling Hall 16
Thomas M Hall 14 <<<<<
Martha E Hall 12
Margaret M Hall 11
Syntha L Hall 9
Malissa A Hall 7
Wm G Hall 5
Lucila J Hall 1
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Name: Thomas M Hall
Age in 1860: 23
Birth Year: abt 1837
Birthplace: Alabama
Home in 1860: Centre Beat, Lauderdale County, Mississippi
Gender: Male
Post Office: Meridian
Household Members: Name / Age
Thomas M Hall 23 <<<<<
Martha E Hall 21
Margaret M Hall 20
Cyntha L Hall 18
Melissa A Hall 15
William C Hall 13
Laceba J Hall 10
Charles Hall 7
Darling Hall 25
Mary Hall 48