The scenic possibilities of this version are simply enormous. Of course, by pure preference, Gilgamesh would be her Servant, in my opinion. She would have managed to summon him by retrieving the key to Babylon that her family has had for a few generations now. (I’m not taking Stranger Fake into account here)
Arturia won’t let Gilgamesh throw away the key when he finds out she has it. Nor will he accept her as his Master for the simple reason that Arturia is only a child and does not praise him in any way worthy of him. But she will not hesitate to use a command seal to make his obey. This will somehow impress Gilgamesh and he will be very curious about her motives. (especially her maturity for her age).
I have already imagined a whole story around these two and in this particular situation. Maybe I’ll share it with you one day ;)
