Try to find him, his children, his wives, his siblings, in the census. If by any chance he lived until the 1925 census, the second page of the image lists parents names and birthplaces. In other census, you can often see parents birthplace, which might help narrow down other census records.
Is this him
"United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MGML-MY2 : accessed 21 March 2018), William Thomas, Swan, Marion, Iowa, United States; citing enumeration district (ED) ED 59, sheet 1A, family 14, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 413; FHL microfilm 1,374,426.
"Iowa, County Marriages, 1838-1934," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:XJK2-MQX : 10 February 2018), Wm. B. Thomas and Samantha M. Miller, 08 May 1877, Marion County, Iowa, United States; citing reference , county courthouses, Iowa; FHL microfilm 986,183.
Lots of William Thomas married a lot of Eliza. Finding a death date for Samantha might help, Finding a divorce record is much more difficult.