If William Wall was his grandfather you might start with who his father might have been. I have William Wall in my tree and have traced the family down through his youngest son Edward Thomas (or Thomas Edward as he was later known as). William's eldest son was George Edward who I believe married Ann Cox in 1836. In 1855 they had a son registered as William J where the J could be John or James. Later in life he may well have switched his name around to avoid the William (as his grandfather William was a First Fleet convict and is thought to have hung himself in 1821).
It seems that George and Ann spent most of their lives on the mid-North Coast, on the Manning River somewhere around Taree. I cant find any record of his son's death in NSW but haven't tried other States. Glad to help if you have even the smallest piece of information about him.