in the empire server when youre making the bet you gotta choose to "test her gag reflex" if you win the bet if you dont choose that option you loose out on her path, thats what happened to me on my first playthrough, hope this helps
The only option I saw is the ticket and giving six eternals and then everything else was for the red head
yeah then you might have to get her affection for you up by choosing different options earlier in the game, sorry hope you figure it out.
im pretty sure there's a guide floating around somewhere I had trouble on my first playthrough too so i just used the guide to get the ones i missed