Elizabeth Eaton large teaspoon

Good day, friends. I tried to get hold of the Samuel Eaton set of spoons (see topic “Old, old set of teaspoons”), but the asking price proved too high for my meagre budget. I have now managed to secure a teaspoon by Elizabeth Eaton. Please see pic.
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Length: 13.2 cm. Please see the pic of the hallmarks. Year letter T (Old English) = 1854. Fiddle pattern. The maker’s mark is by Elizabeth Eaton, the wife of William Eaton (II), who was the son of William Eaton (I). William Eaton (I) started silversmithing in 1784. He died in 1845. William Eaton (II), born in 1788, started silversmithing in 1813 up until 1845. He married Elizabeth and they had a son. He went on to become one of the most prolific silversmiths in the country. William (II) registered his marks “W.E” and “WE” in 1804 and 1843. He died in 1856. William (II)'s widow Elizabeth registered her mark “EE” in 1847 and 1857. This is as I understand the lineage.
What I would dearly like to establish, is who William (I) descended from. Could it be the Samuel Eaton who made the spoons I missed out on? Samuel Eaton was the uncle of John Eaton. John Eaton became Samuel’s apprentice in 1738. John qualified in 1745. He entered his first mark in 1760, his second mark in 1761, and his third mark in 1762.
Might William (I) have been this John’s son?
Regards
Jan