Head back to Madain Sari. Once there, follow Eiko back to her house. After talking to Vivi, pick up the Survival Vest and Phoenix Down then head to the Eidolon Wall.

Talk to Morrison and have him heal you. Peek inside and the moogles will bring you the contents of the treasure chests: an Exploda and an Elixir. Ask Morrison about Mog, then go save Eiko.

Zidane will end up fighting Scarlet Hair one on one.

After defeating him, return to Eiko's house and talk to her. She takes the jewel with her as the Memory Earring.

Go out to the railing in front of the house and listen to Dagger's song to move things along. When you leave, Amarant will join you.