Leave the rest stop using the horse to continue the story. There are two ways to go about the Lovers fight:
- Go with Jotaro. You won't be able to join the battle with Kakyoin and Polnareff and gain EXP, but you'll get bonus FP with Jotaro. In addition, if your protagonist is female, you'll get an extra scene after Jotaro is thrown out of the jewelry store, which itself will differ if Jotaro's FP is over 9.
- Go with Kakyoin and Polnareff. As long as your Stand isn't Pixies, Napalm Death, Quicksilver, Caravan, or Mr. Big, you'll be able to enter the brain and join the fight against Lovers. If you fool around too long in this fight (like if you get whole-party berserked for a long time), it'll end automatically with no XP/GP gain after a short scene.
Afterwards, you can continue the story by entering the boat shop at the south of the map.