You are on the right track!
Timothy b1811 married Eliza GWILLIAM daughter of James and Elizabeth GWILLIAM in 1840. Here is entry from BMD Index:
Marriages Mar 1840
GUILLIAM Eliza Monmouth 26 75
GUILLIAM Timothy Monmouth 26 75

I regret to say I do not have any more detail. This marriage is not listed in the Parish Records and is most likely to have taken place at a Register Office.

I was not aware that Timothy left these shores but explains the lack of information for him in my database.

Mike