A plausible hypothesis is that the Faulkners, possibly including James C, were children from a prior marriage of Ann B. Sears. Likely, her husband's name was Faulkner. All the children were born in Indiana, except James, who was born about 1829 in Kentucky. Ann B. Sears was born in Virginia. Her first marriage might have been somewhere in Virginia or Kentucky. George, Cyrus, and John were born between about 1835 and about 1839, but births were not registered at the time in Hendricks County. No family Bible has been found. If they lived long enough, death certificates for George, Cyrus, and John might name their father, but at this point research has not yet followed them forward in time.
Still, paternity can be established without doubt from other records. First, a Hendricks County marriage return registers the marriage of Ann B. Fawkner and Wesley Sears 1 September 1841. Since John, Cyrus, and George carried the Fawkner/Faulkner name, it seems likely that a first husband named Fawkner or Faulkner was present in Indiana between about 1835 and 1841. The 1840 U.S. Census enumerated Ann "Fortner" with five minors -- two boys under 5, 1 boy 5-10, 1 boy 10-15, and one girl, 5-10. The younger boys are a reasonable match for John, Cyrus, and George. The older boy could be James C., born about 1829.
With "Faulconer" now added to the mix, the spelling of the family name remains unsettled, but it is now clear that the father of James C. Fawkner and his siblings was John C.Faulkner or some variant such as Faulconer or Fortner.
The family is now anchored in Indiana, but surprises are just around the corner. Tune in again next week when Ann Sear's obituary will throw us for a loop. ("Loop" is a technical genealogical term).
LESSONS: Be alert to blended families and in an era before death certificates find probate or guardianship records that might reveal parent-child relationships.