Although most sources list him as Thomas Barnum (perhaps indicating a personal preference) his grave marker shows him as Joseph T. Barnum and he appears in at least one other source as Joseph Thomas Barnum.
Thomas Barnum was enumerated in the 1864 Census of the Territory of Arizona, as follows:
Thomas Barnum, 32, M, Single, b. New York, 3 months living in the territory
Thomas Barnum received a homestead patent in Arizona. The patent description in BLM records is as follows: Patentee: Thomas Barnum; Survey State: Arizona; Acres: 156.53; Metes/Bounds: No; Title Transfer Issue Date: 4/10/1874; Land Office: This record has not been checked against the Legal Land Patent; Cancelled: No; US Reservations: No; Mineral Reservations: No; Authority: April 24, 1820: Sale-Cash Entry (3 Stat. 566); Document Nr.: 6; Accession/Serial Nr.: AZAZAA 014125; BLM Serial Nr.: AZAZAA 014125.
In the 1870 US Census for Salt River Valley, Yavapai, Arizona the family of Thomas Barnum was enumerated as follows:
Household #4; Family #1
Barnum, T; 38; M; W; Farmer; b. New York
Barnum, J. J.; 21; F; W; House Keeper; b. Kentucky
Barnum, H. E.; 4; F; W; b. Arizona
Barnum, L. A.; 2; F; W; b. Arizona
Leonard, T.; 40; M; W; Wagon Maker; b. Ireland; father and mother foreign born
Inscription: 1st Elected Sheriff of Maricopa County, May 1871 (5 sons buried in lot).