If you do a search for Thomas Elliott in White, Illinois, United States... it should come up as on page 17 of 60 (Incidentally, our Hannah Russell-Manley-Jones is at the top of page 15 of 60).
As listed here, the head of household is Byrum Elliott, born in Illinois in August 1850.His wife, Mary E. Elliott, born in IL in Dec 1853. Next is his son Arthur, born in IL in Aug 1873. Next is Byrum's daughter-in-law Bessie M., born in IL in Jan. 1881. Next is their grandson Byrum, born in IL in Sept. 1898.And lastly, their grandson Thomas H., born in IL in Dec. 1899.
I know you were looking for the son of Byrum and not the grandson, but perhaps this is the man you were looking for?I hope this can be of some help to you.