Krile can follow the aetheric trail, but only if Master Matoya gives permission to use the Crystal Eye.
Requirements
This quest is available if you have completed the quest Another Time, Another Place.
Starting the Quest
Talk to Krile in the Dravanian Hinterlands to begin the quest.
Enter Matoya's Cave
Go to the quest icon on the map and check on the Cave Entrance to go into the cave. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.
Speak with Alphinaud
Go to Tailfeather and go to the quest icon on the map. Talk to Alphinaud to proceed.
Show Alphinaud's Sketch
Go west into Tailfeather and go to the nearby quest icon to find Loupard. Talk to him and hand over Alphinaud's Sketch.
Go northwest across the small bridge and enter the house on the other side. Talk to Marcechamp and hand over Alphinaud's Sketch.
Go outside and go south to the quest icon on the map. Talk to Grimold and hand over Alphinaud's Sketch.
Speak with Krile
Go north to the quest icon on the map and talk to Krile.
Wait with Krile
Go northwest to where the orange arrow is pointing in the minimap. Check on the sparkling Destination to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Alphinaud to accept the next quest: A Little Slow, a Little Late.