Having My Galatic Penic Champion as a male through this game, I set my rival rival to be female, because I expected to be boning her right-quick.
I, however, was delightfully surprised to find I was not. Instead, Jill comes off as a bit of a tease, to me. I imagine her waiting for you so she can rub it in your face that she beat you. If she would have gotten the probe on Tarkus you know she would have waited for you, JUST so she could mock you for your incompetence before blasting off into space and "Forgetting" a small clue that would lead you to her next location.
You see, Jill is actually suffering from a sever case of "Notice Me Senpai!". Being the the prodigy tool of Max, she has only ever been recognized for her accomplishments, not her humanity(Or lack there-of). She wants to be recognized for how well SHE is doing, not how well she is at DOING. But our poor, innocent (LOLOLOLOL!) Jill has never learned how to properly express her emotions and the like to the the cloistered up-bringing she has had that morphed her into the uber-bitch she is today.
So, when push finally comes to shove[ing Jill face down on the ground....] I feel like Jill, being the smart cookie she is, would realize her defeat and give in to the PC on the condition that she gets to be their "secretary". Afterall, Jill is smart, knows her way around business better than you. It only makes sense that an idiot like you keep her around. (Read: I-it's not like I WANT to be around you~! I just don't want Max getting anything! B-Baka!")
Jill would then be instated as my adorable Tsundere Secretary Maid. Until she comes to accept you as her superior, she's really only good for being a B**** to you (Just like old times....). But When Heroguy finally calls Jill out on her feelings, she, of course while denying it all, gives in, and some very sweet, tender loving making transpires. After that, Jill opens up a bit more and becomes more useful as a crew member; She would be very valuable in deduction and manipulation of key power players on more populated planets, always being sure to remind me just how much of a failure I am and how much she is valuable to me. On planets like our up-and-coming Snowy Abyss? Useless as f***. With a bit more sexual confidence, we'll slip a threesome with Anno in there too. Afterall, Anno did get it on with your dad...and you...why not collect them all?!!?