Well I'll try.
2nd Lt John Brown enlisted as a 22 y/o in Capt Amos Hullet's Company (M?) of 1st NE Cav July 27, 1862 sworn Col. Pointdexter at Boone Co, MO. Elected to rank Aug 2, 1862. Appears on muster card as present in Aug and Dec 31, 1862.
He is clearly not the same John E Brown in Co F. in Will's Co enlisted Monroe Co, nor is he John F Brown 26 y/o in Ely's Co enlisted Monroe County Aug 1862 who was captured in Montgomery County Dec 1 1862. He was exchanged City Point Summer of 63.
So I come up with John Brown, Son of James Brown born 1840. Living in Boone County. This is not John Isham Brown Sr of Audrain County! He was son of Thomas Brown and has draft record July 1863.
1850 Census
Name: John Brown
Gender: Male
Age: 10
Birth Year: abt 1840
Birthplace: Missouri
Home in 1850: District 8, Boone, Missouri, USA
Attended School: Y
Line Number: 35
Dwelling Number: 1807
Family Number: 1807
Household Members:
Name Age
James Brown 52
Sarah A Brown 35
John Brown 10
Wm Brown 7
James Brown 5
Dudley Brown 3
Berrywick Brown 2
1860 census
Name: John Brown
Age: 21
Birth Year: abt 1839
Gender: Male
Birth Place: Missouri
Home in 1860: Columbia, Boone, Missouri
Dwelling Number: 1323
Family Number: 1275
Household Members:
Name Age
Jas Brown 50
Mary Brown 45
James Brown 23
John Brown 21
Joseph Brown 19
Haden Brown 17
Mollie Brown 16
Susan Brown 12
Annie Brown 8
Martha Brown 5
1870 Census finds him single living in Dooley's Boarding House Columbia MO.
Name: John Brown
Age in 1870: 30
Birth Year: abt 1840
Birthplace: Kentucky
Dwelling Number: 270
Home in 1870: Columbia, Boone, Missouri
Race: White
Gender: Male
Post Office: Columbia
Occupation: Carpenter
Male Citizen over 21: Y
Household Members:
Name Age
Geo R Dooley 65
Nancy Dooley 46
Aubrey Dooley 14
Eugene Dooley 11
Elliott Dooley 7
Amelia Parker 26
George Schmeidtz 28
N C Bicknell 31
John Brown 30
John Morgan 21
Maria Jackson 18
Mary Jackson 4/12
Amelia Peterson 48
Millie Peterson 15
George Peterson 11
The trail goes a little cold but I'll see if I can't tease something out.