Although you have a lead, you will need to win the trust of the Little Ala Mhigans before you can continue your investigation.
This quest is available if you have completed the quest Tea for Three.
Starting the Quest
Talk to Gisilbehrt in Little Ala Mhigo in Southern Thanalan to begin the quest.
Speak with Minfilia
Use a Vesper Bay Aetheryte Ticket (which you received after completing the quest The Scions of the Seventh Dawn) to return to Vesper Bay. Go into the northwest building and enter the Waking Sands. Go into the Solar and talk to Minfilia to complete the quest.
Next Main Scenario Quest
After you complete the quest, you will need to be at least level 26 to proceed to the next quest. After you reach level 26, talk to Minfilia to accept the next quest: Meeting with the Resistance.