So far I have discovered that the word didn't mean "member of a nation" back in 1770, at least not in the English Language usage of the time. It only meant that in the Swiss usage of the time.
I think the more we can demonstrate that the source for that word is not English, but is in fact derived from the Swiss usage of the word, then we can demonstrate categorically where they got their definition of it from, meaning Vattel, Burlamaqui, and Rousseau. (All Swiss writers of Natural law, and all who used the word "Citizen" to describe the members of a nation.)
All English writers of natural law used the word "Subject." (Locke, Rutherford, Hobbes, Lord Summer's Priestly, etc)
I think this word "Citizen" is the key to linking the definition to Vattel.