Hi there,
I will ask the Moderator to move your post to the Aussie Board, rather than leave it here on the Armed Forces Board ....
(*)I will of course try to help you with the thrust of your question.
Edit to add 
I don't live in Sydney, so in the internet age it is perhaps more difficult to research from my armchair than from your Melbourne location. I am somewhat confused as where on the Armed Forces Board here at RChat you have found my comment
"re a resident of the Liverpool Asylum in NSW Australia" but .... here's some thoughts (I have lots more, but these seem sensible to start with)...
Have you checked out the links on the NSW Resources Board,
Have you gone through the NSW SRO indexes
Do you have the 1900 d.c. for your chap, if so what are the details recorded on that, and do those details match up with any previous knowledge you held about that chap, thus comfirming he belongs on your own family tree ...
Cheers JM
(*)Moderator Comment: now split off and moved to Australia board