I think we may have the solution to William S Gidley's origins - a miner who emigrated to California. His gravestone (pictured above, with the useful inscription "died in 1865 aged 40") can be found on the Find A Grave website. The Cornwall Gidleys always looked the most likely, as so many of them sought out further mining opportunities when the Cornish industry collapsed.
Marilyn from the USA contacted me in 2011, and I hope she won't mind me quoting from her email in full:
" We had a wonderful afternoon Sunday, drove to Grass Valley,Ca. Nevada County CA. Checked on my great great grandfather William S.Gidley's headstone. With the steel plate my husband put behind it a few years ago, it is still standing. The cemetery is across the street from St. Mary's Church, but cemetery is not in good shape. Many markers seem to be gone since we were last there. There are rocks around his spot, so I rather think there is another grave there, perhaps his wife Jane Newell although I can find no record of such.
On earlier census he was living in Sierra County, where the 3 children were born, near his in-laws and other Newells. He had a saloon and grocery store in Grass Valley, located on Mill St. (the main one) between Neal and Welch. I have walked that street, Lola Montez had a home there. The area now is Bank, offices, Chamber of Commerce.
I found another William Gidley born 1804 died 3 Nov. 1872 in Gold Hill, Story County, NV. service by St. Paul's Episcopal of VC. His age, he could have been my WSG's father. My Wm's daughters did move to Virginia City, NV."
My best guess at the moment is that Marilyn's ancestor, William S Gidley of Grass Valley, was one of the Cornish Gidleys, the son of Richard Gidley and his wife Bridget nee Simmons. In 1841 this William was a copper miner, at home, Little Killiow, Kea, Cornwall, and after that he vanishes from the UK censuses. The Simmons connection might also account for the S in his name.
William Gidley of Grass Valley was a retail dealer in the California tax returns of 1865, so he gave up mining before he died at the age of 40.
I've been through all the references I have for every William Gidley I've found born from about 1823 - 1828, and the others are all accounted for.
The older William Gidley born in 1804 was probably his much older first cousin William, son of William and Thomasine Thomas, although the records show that this William wasn't christened till 1808. Perhaps the person recording his death in America was not sure of his actual age. In 1841 this William was also a miner, in Gwennap, Cornwall, and then turns up in 1860 and 1870 in the American censuses mining in California. His wife was left behind in Gwennap, describing herself in 1871 as "Wife of husband in California".
However, I should say that William and William Henry were extremely common names with the Cornish Gidleys and I'm certainly not sure that I've got it completely correct.