Just who is the one giving Rei-Q her orders? Does she accept them a particular person or entity, or from anyone at all? In particular, who ordered her to cut off Mark.06's head?
Rei I was ordered to.
1) The obvious answer is of course Gendo. But there is no evidence that Gendo has any connection to Rei-Q whatsoever. The two never speak, and are only once in the same area. In particular, Gendo does not seem to be paying any visits to Rei-Q's tank.
2) The next most obvious candidate is then Seele But if Seele are giving Rei-Q orders, then why bother hijacking Mark.09 with a "program" after she carries it out? Why not just have the program do everything from the beginning?
3) The two most obvious candidates out of the way, I'd like to introduce some "left-field" possibilities. The first, and most unlikely, is Shinji. There's a suggestion earlier in the film that Rei is receptive to Shinji giving her orders, and he may have ordered her to put on clothes when he first goes to speak with her. But since Shinji was hardly aware that Rei-Q was even going down to Central Dogma, this seems extremely unlikely.
4) Kaworu is another possibility, though we never see the two interact. Another difficulty here is that he never gives her further instructions as the situation changes, nor asks for her help as Shinji pulls out the spears. It doesn't seem that he would be in charge of her.
5) Lastly, I'd like to consider one final -- "out there" possibility. What if Rei-Q was taking her orders -- this order -- from Rei-II.
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Apart from Shinji, This is the only other character who Rei-Q "interacts" with prior to the final battle at all. But since I have absolutely no theory under which this would make sense, I'll leave this one hanging in the fan-wankery pantry untii someone eats it or it begins to ripen.
Anyway, I thought that exploring this simple topic might stimulate some thinking.