Cajondy
This is one elusive family! I may have found something from 1861 courtesy of
www.rhiw.com1861
Llanengan
Abode CONGLE CAE
Eleanor Eames Head Widow age 45 Miners Widow
Moses " Son 13
henry Son 7
eleanor Dau 4
Robert Son 2
Robert is the link to the 1881 census entry of Robert Eames 21 Brother in Law showing that he is William Eames brother and therefore "in law" to Margaret (b 1845). This seems to confirm your find of William's parents being John and Eleanor as Eleanor is shown above as a widow!
BMD entries for Pwllheli tend to confirm this too with a Robert Eames birth registered in 1858 - also registered in that district are William 1838, John 1840, dorothy 1842, evan 1845 and John 1861. Now whether they all share the same parents is a different thing ....a few do I am sure.
Also in the 1861 census transcrioption on rhiw.com website is
Dorothy Eames ( links to the one on BMD) age 17 Gen Serv Unm b Lanengan living at TY CAPEL
John Eames ditto age 20 Servant Unm b llanengan living at PENRHYN MAWR
Evan Eames ditto age 16 visiting PENRHYN MAWR
Like a say they may be related they may be not. Having found Penrhyn Mawr on a map it is not too far from where William b 1838 was born as shown on his birth cert - i think you have the right one!
Death certs for William Eames is Jun 1909 aged 69 puts dob at 1840-ish (Bangor 11b p 309)
Margaret Eames is Mar 1919 aged 74 puts DOB at 1845-ish (Bangor 11b p792)
the death certs may give a further clue as to where they are buried.
William Eames and Margaret Williams marriage - the connection on how they met may be found thanks to the vessel William is on in the 1881census. The boat was registered at Beaumaris in 1866.......owner William Williams and in 1873 Mr Williams lets his new son in law captain the boat.
A most tenuous jump of faith this but one i think worth you investigating - the dates just tie in too well - see this at the following (National Archvies)
http://www.nationalarchives.gov.uk/a2a/records.aspx?cat=221-wdb&cid=314#314This may raise more questions than answers but at least it is hopefully a little progress for you
Mair