...... To simply disappear from records for 45 years in the 20th century takes some doing.
I agree with shume ....
Disappear in the Central West of New South Wales between say 1914 (commencement WWI) to death in 1959 ... Yes, very possible that you cannot find records for him in that era in NSW. You have him born Galway, Ireland. It was still possible to 'disappear' in NSW records even in the 1940s, and perhaps up until late 1980s when 100 points for ID rules came around.
a) He may not have been in NSW until shortly before his death ... NSW death certs (or the cheaper version, 'official transcription') have space for 'how long in the colonies/states ...
b) In NSW it became compulsory to enrol to vote in state elections in the 1920s if you were a British Subject, aged 21 and over, resident in NSW, not in gaol, not a bankrupt ... etc . I think Galway would be in the Republic of Ireland, and in the 1920s it separated from British rule, so it may be that he was 'staunch' Irish, and may not have considered he was a British Subject, so choose not to enrol.
c) He may have become known by a different name ... no need to provide proof of name at that time, just become known as ..... (still possible, but now it is quite difficult)
ADD
WWI enlistment ... AIF ... not compulsory to enlist, all volunteers, two referendums on conscription during the war, both times the NO vote succeeded.
JM