There look to be 63 deaths registered in the name of 'James Anderson' in VIC between 1856 and 1878!
Have you seen the 7 page Will and 3 page Inventory for Margaret Rowan Anderson on SP?
I wonder if this snippet might be worth investigating:
MR. JAMES ANDERSON, Artist, supposed to be in Sydney, New South Wales, is requested to communicate with Messrs. CLAYTON and ATKINSON, Solicitor, Melbourne, who has communications from his relative, Sir James Anderson, of Glasgow, requiring his immediate attention.
The Sydney Morning Herald, Thursday 1 September 1859