Perfection Lab Aftergame Confusion

I’m trying to complete Reukra’s storyline (I’ve done all aftergame quests besides this), and I have no clue where to go next. I went into the Perfection Base and found the note talking about the secont start and how something was in Amphitrite City. Beyond that I’m stuck. What do I do?

Did you go to the crystal caves?

I did for the timeless, but now I’m realizing I should’ve actually looked there as well. oops