The SSDI and California Death records show his birthdate as Dec 1905, which doesn't quite agree with the 1910 census (he was recorded as being 1, therefore born in 1909), 1920 census (he was recorded as being 11, therefore born in 1909).  However, it does agree with the 1930 census (he was recorded as being 24, and since this census was taken on April 23, 1930, this is how old he would have been if he were born in Dec 1905). I think he was probably born around 1908 rather than 1905.  The 1910 census shows him to be 1; it is not likely that the family would make a mistake of four years on such a young child.  Likewise the 1920 census shows him to be 11 and it isn't likely that a family would think he was 11 if he was really 15. However, the census shows that his father died when he was a child and he was raised by his mother and step-father, John Kemper. It is not unlikely that he just didn’t know his age when he reported for the 1930 census and that he continued to believe that he was 3-4 years older as he grew to adulthood.

1920 Census of St Louis MO
Name Age
John Kemper 38 head
Lavina I Kemper 42 wife IL IL IL
John Kemper 14 son
Birdie Kemper 10 dau
James R Heathcock 11 step-son IL IL IL

1930 Census of Detroit, Wayne Co MI
Name Age
James R Heathcock 24 b IL
Isabel Heathcock 19 b MT
Eugene W Heathcock 1 1/12 b MI