His gravestone says 1858-1943.2946 This must be wrong as the 1860 census recorded him as being 7 years old. Likely someone misread 1853 as being 1858 when the gravestone (which appears to be recent) was carved.

1860 Census of Burnet, TX

Name Age
Alford W Conner 35 AR
Lucinda Conner 33 IL
Eliza A Conner 14 AR
Sarah J Conner 13 AR
Mary E Conner 11 TX
Wm B Conner 7 TX
Malinda C Conner 5 TX
Samuel S Conner 3 TX
Charles K Conner 1 TX

Burnet County was founded in 1852 and later organized in 1854.[3] It is named for David Gouverneur Burnet, the first (provisional) president of the Republic of Texas. The population in 1860 was 2487.2947

1870 Census of San Saba Co TX

Name Age
Alfred Conner 45
L Ann Conner 40
William B Conner 16
Charlotte M Conner 14
John S Conner 12
Andrew J Conner 11
Charlie Conner 10
S antny Conner 8
Aurelius Conner 2

In 1856 San Saba County was organized from Bexar County and named for the San Saba River. San Saba was selected as the county seat. The populatioin in 1860 was 913 and in 1870 was 1425.2948

1880 Census of Brown Co TX

Name Age
Wm. B. Conner 27 TX farmer
M. E. Conner 22 TN
Dolly J. Conner 5 TX
Delila A. Conner 3 TX
E. S. Conner 1 TX
N. E. Eply 26 TN (brother-in-law)

Brown County was formed on the western frontier in 1856 from Comanche and Travis counties and organized in 1858, with Brownwood designated as the county seat; the town was also awarded the county's first post office that year with Wiley B. Brown as postmaster.2949

1900 Census of Lerdsberg, Grant Co NM

Name Age
William R Conner 47 Apr 1853 TX AR PA
Mary E Conner 42 Mar 1858 TN TN KY
Ira C Conner 16 Mar 1884 AZ TX TN
Charles Conner 14 Nov 1886 AZ TX TN
Mary Conner 11 Jun 1888 NM TX TN
W Henry Conner 3 Jul 1896 NM TX TN
Benjamin Dunigan 8 Mar 1892 NM TX TX (grandson)

1910 Census of Hachita, Grant Co NM

Name Age
Wm B Conner 56 TX AR PA
Mary E Conner 51 TN TN KY
Charles A Conner 23 AZ TX TN
Henry Wm Conner 13 NM TX TN

1920 Census of Animas, Hidalgo Co NM

Name Age
William B Conner 66 TX AR AR

1930 Census of Lordsburg, Hidalgo Co NM

Name Age
Henry Conner 33
Nettie Conner 29
Laurford Conner 10
Billie Conner 7
Eugene Conner 3 5/12
W B Conner 76 TX TX TX (father)