Dorrie,
Many thanks for your continued interest in the mystery.
William doesn't show up on FindMyPast in the 1911 census, for some reason.
In his son Fredrick's first (legitimate) marriage certificate in Gorebridge, in 1889, his father is described as a labourer. One would have thought that this was correct as there was no reason to lie. Although William had been part owner of a mine, a publican and a manager, it would be concistent that this was the only job he could have got after leaving England, wherever he was.
In Frederick's second, bigamous, marriage certificate in Edinburgh, in 1900, his father is correctly named as William, but his occupation is "manager of oil works." William had in fact been a manager for one year of an oil works in Wales. This might have been Frederick picking the most prestigious sounding of his father's occupations, but with the record of a William Davies, a tenant of Pumpherston oil works, I thought the oil works part might at least be true. But your discovery of another William Davies, a shale miner, who must have been employed by the Pumpherston oil company, makes it very doubtful, particularly as there weren't many William Davieses in Sctoland.
However there is still a bit of a mystery, particularly the fact that William Davies from Airdrie does not seem to have left home until after 1891, while a William Davies was a tenant of Pumpherston oill company, in 1881 onwards, and 1892 to 1894. The address of the latter also appeared to be in Pumpherston and not in Uphall.
Frederick finally married in 1928, in Wakefield, Yorkshire, (still technically bigamously), but i haven't got the certicicate. I would think that it would probably say "father deceased."
There dosen't seem to be any other records of personal details of the employees of the oil company and I can't think of any way forward. It leaves me with a lot of doubt and still longing to know how and where my great grandfather finished his days. I have also wondered if he married again and I had more relatives somewhere else in the world.
Don