Hi
You haven't told us what date he died so we can't work out a birthyear from his age at death. Without knowing his birthyear it's virtually impossible to find anything on him
You haven't told us his wife's name or where she was born or when and where they married
Presume he died in Australia??
You say he left his wife and son in Perth WA to travel to the goldfields of WA but death cert says
wife & 2 daughters somewhere in Yks
Does this mean you suspect he may have been a bigamist?
Have you checked passenger lists to find the date he emigrated to Australia as it is no use us trying to find him on a census if he was not in this country at that time
Your post gives the impression that he was born in Lincolnshire as you made no mention of the Yorkshire details from his death cert or the fact that he was not living in England at the time of his death.