I find him on the 1860 Federal Census, but none others for either he of any other family member.

No wonder, his widow married James Rogers who adopted the children who took his name.

You might check the interments in the Confederate Cemetery at Fayettville, Ark. See: http://www.exploresouthernhistory.com/fayettevillecc.html

He doesn't appear to be listed among the known buried.

.....

This is the one and only muster roll for Ambrose Fair's [sic] company, his presence was not stated although recorded on the list of men enrolled.

Capt. Moore's Company, Adams Regiment Infantry, 2nd Brigade, Arkansas Volunteers, called into the service of the Confederate States in the Provisional Army under the Provisions of the Acts Congress passed February 1861. Enrollments from the Eleventh day of August 1862 (date of this muster) September 12, 1862, for the term of the war unless sooner discharged.

Dated Sept. 12, 1862, Elm Springs, Washington County, Ark.

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1860 United States Federal Census about Ambrose Farr
Name: Ambrose Farr
Age in 1860: 26
Birth Year: abt 1834
Birthplace: North Carolina
Home in 1860: Kings River, Madison, Arkansas
Gender: Male
Post Office: Kingston
Value of real estate: View image
Household Members:
Name Age
Ambrose Farr 26 Farmer
Milly Farr 25
Reuben Farr 5
Wm Farr 3
Jerry Farr 5/12