The Ship Who Searched, by Anne McCaffrey
And continuing my re-reading kick... another in the Ship series by Anne McCaffrey.
The brain in this one is Tia and this time there's a consistent brawn too, Alex.
Tia is quite a bit different than the other brains in the series so far (and after for that matter) in that she's 7 or 8 (I don't remember exactly without looking it up) before she becomes a shell-person. And it takes some significant doing by a doctor and another shell-person to get her in the program in the first place.
Once she's ensconsed in her ship, the searching refers to her attempt to find out what made her sick (forcing the whole shell thing) and make sure it doesn't happen to anyone else.