Ok, got stuck in that same part in goddamn brothel sequence again, finally found what it took to progress. Which is, going to the restaurant at evening, having a glimpse of Alex, sleeping and then finding the hanging of crescent moon the next day at the main road.
This was so goddamn unintuitive, because the event sort of presumes that you were sleeping at the hotel and went at evening, Sarah says she sees Alex in the garden, but when you go, there is no one to be found besides those flirty guys from the beach.
Its really hard for you to stumble into that because: 1) if you're doing the brothel scenes you just sleep with gunram and never usually go out at evening 2) the hotel is expensive and you usually wouldn't sleep there anyway, even before getting the certificate.
From what it looks on the guide there isn't that much going on after this part either. Oh and btw, there is a breaking bug that happens when sleeping in the inn next to the hotel, if you the bed from the side, the walks two squares and gets stuck on the other bed, if she uses it from below, it comes out normally, but it doesn't have clothes in the bin, meaning you can never leave the room.