Hi,
William Chalmers does not want to be found! His wife Ruth Matida didn't help me, find him, either.
1932, 33, 34, 36 & 37 - NSW Electoral roll for Ruth Chalmers, Rawson Road Smithfield, NSW. On the 1934 Roll a William Kirkpatrick Chalmers is living at the same address, as Ruth. I can't find a NSW death to confirm this is William's wife / ex wife.
1925 Qld Elect Roll - Ruth & William Chalmers (engine driver) but after further research I dismissed this as I think this Ruth was nee Riley.
I hoped William might be found with his brother Walter in NSW, but I suspect you have already been down that dead end road.
William's siblings death notices, & living descendants of those siblings, would be the track I'd take, hoping someone can shed light on Great Uncle William's Life.
Sorry I'm no help. but I can't stop "playing with" your very interesting family. Feel free to PM me if you want to discuss any possible theories.
Cheers.
Valsgirl