Asmodia gets in on it, barely on time, and manages to give Keltham an inquiring look about whether it's her turn that hopefully didn't come across as being at pleading or requesting, which might look suspicious to anyone considering the course of events later.
Once she's been tapped, she diligently goes off to her room to think, reviewing Keltham-lecture notes so that her thoughts won't look too suspiciously empty.
The Wisdom isn't there to provide realizations, it's there to provide an excuse for having had them.
Some of her plans refine themselves further anyways; she puts what of the thoughts she can outside of her barrier, it is fine and good for Security to see those.