The One Ring would be the reason he is brought back, Eru or the Valar (whoever sent Glorfindel) would be the one(s) to actually send Gil-galad back, which could have happened.
No, actually
Every 'what if' situation of all the other factions is based essentially on 'real' possibilities, though very strange and improbable.
Because Gandalf, Théoden, Saruman (and the other ring heroes) really had the possibility (even if it was really slight) to achieve the One Ring.
The Valar, after the War of Wrath, decided not to intervene anymore in the World, fearing other possible destructions.
They, then, 'only' sent the Wizards to guide the Free People of Middle Earth and Glorfindel, as a really unexpected exception, because every Elf who lives or was reborn in Valinor can't return to Middle Earth; this is an absolute rule of Valinor, there is thus no possibility or any space for 'what if' situations in the first place.
Not to mention that we don't know if Gil-galad was actually ever reborn in Valinor or he is still mourning in the Halls of Mandos as a spirit.
Gil-galad has his reasons in being implemented through the Last Alliance spell, along with his allies of Arnor and Gondor; this is an unique and characteristic spell of Rivendell that refers to the Second Age.
The One Ring can't bring anyone back from Valinor, since the power of the Valar is far beyond it.