From Trove (Free online Australia newspapers)
https://trove.nla.gov.au/newspaper/article/22490917?searchTerm=%22william%20hugh%20brent%22He is charged with vagrancy 24 June 1905 aged about 75 and asked to go to another Benevolent Asylum as he had been at Ballarat and Geelong.
From Ancestry.com.au
1875-76 admitted Liverpool Asylum NSW age 72/73 Vagrancy occupation ? Blacksmith
1900 Charged Newcastle NSW Exposing his person - Not Guilty
You can find patient records for each asylum on
https://prov.vic.gov.au/explore-collection/explore-topic/health-and-welfare/mental-health-records-1849-1912But its a long haul through the different asylums!
I can't find a death for him as yet and if he died in an asylum it would have been registered
re Immigration there is a convict record for a William Brent arrived 1831, estimated birth 1807. Might be worth checking out.