Actually, I'm 'solicitr'; and I think there are two theories of Elvish (or Noldorin) succession, either of which could explain the known data, but the "eldest male" theory seems to fit
all the data better.
A) The succession can pass via the female line in the absence of a son, but not to a female in her own right.
B) The succession passes to the eldest male member of the Royal House
Theory A explains almost everything, including Finrod's title passing to his nephew rather than his sister Galadriel (older than A&A), Turgon's High-Kingship passing to his grandson Earendil not his daughter Idril, Thingol's Heir being his grandson Dior not his daughter Luthien, etc.
However, A comes a cropper under these 3 circumstances:
- Gil-Galad is Fingon's son
- Gil-Galad is Finrod's son
- Gil-galad is Finrod's nephew or great-nephew
In Case 1, Gil-Galad should have become king after the Nirnaeth, not Turgon. In Cases 2 and 3, Elrond as Turgon's great-grandson, distaff or not, would have had a superior claim to any Finarfinian.
And this is why I tend to favor Theory B. It doesn't matter whose son Gil-Galad is; the succession went to the eldest male of the House of Finwe in Middle-earth (not counting the disinherited Feanorians). Had Nargothrond held out longer than Gondolin, Orodreth would have held the title, no matter how briefly, and even if G-G was Fingon's or Finrod's son.
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Of course, externally one can trace how Tolkien created a knot for himself (cf. the matter of female succession in Numenor): it was a given from the time of the Sketch that Turgon succeeded his brother Fingon, and after that it didn't matter because there was no Gil-Galad and for that matter no Second and Third Ages. Since Turgon's family was pretty much set in stone, Gil-Galad like Galadriel had to be shoehorned in somewhere else thanks to the LR.