Have you found William's marriage cert to Mary Ellen that should confirm his father's name and occupation?? On your previous thread Galium suggested
"There is no Jane Monaghan (daughter of William) birth registered anywhere in England and Wales during 1887/8.
However, the birth of Jane Jackson registered in West Derby district (includes Garston) in December Q of 1887.
Jane Jackson d/o Thomas and Mary Elizabeth* was baptised 11 October 1887 at St Michael, Garston. Thomas is a labourer and the family live at Windon Lane, Garston.
*Thomas Jackson married Mary Ellen Hughes at St Peter Liverpool in 1887.
Sorry, this isn't helping you find William, but it's possible that his wife is Mary Ellen Hughes, not Jones."
Since this thread the GRO Birth index is now available which gives the mothers maiden name and I think his son James Henry b about 1889 Gaston is
JAMES HENRY MONAGHON mothers maiden name HUGHES
GRO 1890 M Quarter 1890 in WEST DERBY Vol 08B Page 626
If William's wife's original maiden name was Hughes then this transcribed marriage that Galium suggested from Anc does look likely and lists his father as John Monaghan
William Monaghan to Mary Ellen Jackson
Marriage 11 Mar 1889 Liverpool, Lancaster, England
Father - John Monaghan
Spouse's father - James Hughes
Not that it helps much at the moment

Kay