William Mayes born Sept 1862 but may be recorded five years either side – he visited Australia with Elizabeth his wife around 1892 when their daughter Jane was born in Sydney
No birth registered in NSW for a Jane with parents Wm and Elizabeth.
Not having any luck with passenger information.
I can't locate Wm with wife Elizabeth and son Wm G. born c1894 on the 1910 USA census.  
Australian Electoral Roll
1930
MAYES William 60 Alpha Road, Chatswood  Buyer
MAYES William Greeley  60 Alpha Road, Chatswood Storekeeper
1936
MAYES William  65 Mowbray Road, Chatswood  Buyer
MAYES William Greeley  65 Mowbray Road, Chatswood  Storekeeper
1949
MAYES Caroline Lucy 55 Durham Street, Hurstville  Nurse
MAYES William Greeley  55 Durham Street, Hurstville  Public Servant
Death notice for William MAYES in 1942 - died at his daughter's residence aged 80 years.
http://www.rootschat.com/links/0fal/16979/1942    
MAYES William
Father John  Mother not known
District Chatswood 
http://www.ryersonindex.org/MAYES Caroline Lucy
Death 6 Apr 2001
Late of Hurstville published in the 
Sydney Morning Herald 9 Apr 2001 
Will have another look at this later.
Cheers
Cando