Hi Glenn,
The William Webster I'm interested in was born in Lancashire in 1843, married Ann Glasgow in Bendigo in 1866 and possibly died in Bendigo in 1913, I'm assuming that this could be your father's grandfather.
The only problem could be that according to what I've been able to find out so far he and Ann Glasgow had three children, Isabella, Agnes and Thomas James, so no child named William as far as I'm aware.
From the Bendigo cemetery records:
WEBSTER, WILLIAM
Date of Death: not available
Date of Burial: 12/06/1912
Interment Number: 21583
Cemetery: BENDIGO
Section: MON M6
Grave Number: 12881
_____________________
WEBSTER, WILLIAM
Date of Death: not available
Date of Burial: 26/08/1913
Interment Number: 22105
Cemetery: BENDIGO
Section: MON F1
Grave Number: 22105
_________________________
WEBSTER, WILLIAM
Date of Death: not available
Date of Burial: 19/11/1917
Interment Number: 23705
Cemetery: BENDIGO
Section: MON L3
Grave Number: 23705
__________________________
There seems to be three possibilities for your great grandfather.
Hope this helps.