William was born on Feb 24, 1822 in Nelson County, Kentucky. The Kentucky requirement for recording births was enacted in 1852 but this was interrupted by the Civil War. Recording began again in 1911. There may be church records but nothing yet.
Elisha died intestate so not much luck there. There are some administrative accounts but they have been no help.
The first census that list the names of children along with parents occurred in 1850 but William and Elizabeth had been married in 1849 and they were not living in the same household with Elisha. .
Because I wanted to know where the Gates' land was located I started to look for some land deeds. And there it was.
An 1855 deed states “This Indenture made this 10th day of October in the year 1855 between Elisha Gates of the County of Nelson and Commonwealth of Kentucky of the one part and William R. Gates of the County and Commonwealth aforesaid and John G. Gates of the state of Texas of the other part. Witnesseth. that the said Elisha Gates for and in consideration of the natural love and affection he has the said William R. Gates and John G. Gates his children…”
Nelson County, Kentucky Deeds
Book 29 page 345
FHL Film 483138