Head back to the Eschalot and fly to the objective marker. Land on the lake and get off the dock. Enter the nearest location in the world map to continue with the story. The group will spend the night away at the Sage's place. After learning of the rainbow thread's location, you're free to leave and search for it. A new party chat will be available as well. (Such Sweet Sorrow)
Before leaving, check the room to the left of the sewing machine to get a Peace Ring. You can also sleep for free in the bedroom to the east so you can grind in the world map if you want. There's a hidden Antarctic Wind in the bucket beside the wooden bridge, and a fox that acts as an all-around shop.
The fox also sells Mythril equipment which is worth getting at this point, provided that you have the cash. You can also find an adventurer here to help you save or access Norende-exclusive goods. Leave the area and head to the cave west of the lake. You have to circle around to the east to reach your destination.