Listen, this isn't just about developing a psionic. Jeyne has gotten it into her head that developing her own personal power is the end-goal of her training but, to be blunt, that isn't what we need. And by 'we' I mean both Viserys personally and the Imperium as a whole. Having Jeyne train with the Githzerai would serve several important purposes at once. It diversifies our relationship with the Githzerai through means other than trade and military force. It allows Jeyne to grow her power both more safely and, more importantly, more consistently. And, perhaps most important, ensures that Jeyne's psionic powers will grow in a way that diverges from her more illithid-inclined nature.
Jeyne has repeatedly expressed concerns about who and what she is. I see no reason to encourage her to turn down training and risk returning to a bad place when there are gentler alternatives. Especially when the reason Jeyne thinks she needs to go it on her own simply aren't valid. By no means should we order her to train with the Githzerai, but we should make it clear that we neither need nor want her to struggle through hardship for the sake of raw power. We should make sure that kind of ruggedly independent, self-tutoring is something she wants for herself rather than what she think is expected of someone in her position.
[X] Point out that you did not have the chance to train when you were in her shoes, but that is no reason for her to deny the chance.