Just curious, Reiichu, but has it been confirmed that Kaworu took control of Eva 13 at that time and had it perform the action, or was the eva going on auto pilot? I'm just curious because just like Mk.09 became independent after via awakening, I thought the awakening of Eva 13 made it instinctually perform the impalements just like the MP Evas in EoE. Because after it noms Angel 12's core it begins to ascend of its own will, against Shinji's will (who was in control at the time) and Kaworu's (who was still locked out minutes before the awakening). I thought the only thing Kaworu did when he gained control was to sacrifice himself to deactivate Eva 13.
Join tempos, make sure that you're both trying to do the same thing, and let the magic happen. If somebody wants to shut the other person out, it would probably work like one of those dual-steering wheel student cars.
Also, I think Shinji's and Kaworu's conflict of control was not jut Gendo's doing but also the fact that Shinji's will to proceed was greater than Kaworu's, which Gendo probably calculated for in the first place. This analogy helps a lot explaining it, because at the beginning Shinji and Kaworu were united in tempos (desires/thoughts) but after noticing the spears Kaworu lost his focus while Shinji pressed on. Kaworu's lagging behind in will to proceed probably caused him to be outranked by Shinji in terms of who Eva 13 was controlled by, and thus as Shinji's will grew stronger Kaworu was eventually shut out as Shinji was proving to be able to handle things by himself. Kinda like how 2 tempos are meeting but when 1 falls behind, the one who is able to keep going become the lead until the other is able to catch up.