Maybe...she had an idea.  It would prove, once and for all, whether or not Cheshire was still in there, in some sense.  Of course, if he wasn't there, then Ishi knew she would be placed on an express train to Slut-Town.  She would tease her, challenge her, drop a hint enough that she had done something to Akiko, or that she'd done something as Akiko.  That would get the ball rolling.