I don't know, but it does sound like Se a little.
It sounds like she wouldn't even know if she was SEI or ESI though. I knew a supervisor relationship between an SEI and an LSE. The LSE would try and get the SEI involved in whatever tasks they were doing and he would get mad at her for not anticipating what needed to be done. He needed to spell everything out and they would get mad at each other. Their relationship didn't last, even though she admired his Te.
So, just a thought, but maybe you could try doing something Te heavy and she if she's receptive or not?
And since I'm living vicariously through you, let us know how it turns out.