William LEE where did you go after 1911?

[Bob Campbell]

 As a follow on to my Henry John LEE topic I have his brother William LEE who was registered at Tottenham in 1885 25th April as Tomas William LEE parents John LEE and Elizabeth Julia PICKERING, last seen in the 1911 census for Gordon Road, Edmonton as a 26 year old, single, piano forte worker. He also appears to have done a runner.
 Generally went by the name just William, or in one census as William T.
Have checked all the possible and most likely deaths and marriages etc, local electoral rolls etc
 No record of him on his mother 1916 and father 1921 death certs. So far he doesn't seem to be a WW1 casualty including the obvious record of a William LEE who died in July 1917, same birthplace/residence. I have not found on passenger lists and he does not appear on the 1939 Identity Registration.
Ideas anyone?