NOTE TO Franz: All of this information here in the 'Main Quest' lore pages is not known by the NPCs unless they are specifically mentioned to know about a piece of information.
Returning to @Gilbert Bates and telling him the news, he will offer to pay you 300 gold (which you can negotiate up to 400) to investigate further. He suggests you visit Edward Teach in Ashbury. He can take you to the @Isle of Despair. Pick up the book on the wharf before you go, it can help.
Once there, talking with the guards reveals you must talk with @Thorvald Two Stones. To talk to him you must get past his guard Orgin Big Fist.
Possible solutions:
Use your lockpick skills to break in
Fight in the pits to prove your worth (if you continue going back to the pits, eventually no-one will fight you anymore and you get the reputation of pit-master).
You can convince him to let you in (the book you found on the wharf can help you in this as he enjoys a good read).
Once inside you need to talk with @Thorvald Two Stones to get more information of the whereabouts of the @Black Mountain Clan. You find out that the @Black Mountain Clan were never on the @Isle of Despair and should talk more with the @Wheel Clan leader @Loghaire Thunder Stone.
Solutions depend a lot on your abilities.
You can kill him
Pick the lock to his chest (in there you will find a book telling you of the location of the @Wheel Clan and the schematics for the special glasses required). After leaving the island, if you cannot use the schematics, in this case you need to go to Raymond’s Fine Spectacles on the wharf and he will make them for you for 1000 gold.
Pick pocket his glasses
Convince him to join with you
Convince him to give you his spectacles
Pay him to give you the information you require.
Once leaving you will find that Captain Teach has had a few “minor” problems with the locals and he can now take you back to Ashbury.
You can go back to @Gilbert Bates and keep him posted and get your pay. When you are ready, you should head to the @Wheel Clan in the @Grey Mountains.