While searching the St James, Toxteth Park records for any references to Stock, Fazakerley or Taylor surnames, I came across a marriage record for William Stock, bachelor, cordwainer of Walton on the Hill, dated 07 Feb 1814.He married Elizabeth Pennington.
I was specifically searching for the marriage record of my ggg grandfather James Stock who married Grace Fazakerley there 22 Apr 1815.
So far I have not come across any Stock baptisms in this parish.James and Grace's first 4 children were baptised at St Swithin Roman Catholic church, Gill Moss.It seems that in order for the marriage to be legally registered it had to be performed in a Church of England.
The witnesses to the baptism of one of the children were John Stock and his wife Dorothy Melling.Their daughter Joanne was married at St Swithin in 1840.
I have yet to uncover any evidence of a relationship between these 3 Stock men.Also can't say a relationship exists between your William and any of these 3, but my line certainly re-used the same forenames, for generations!
I'll keep you updated with anything I discover; please do the same.