Buckthorn will take one last look at the a pile of skulls in the chamber (the one where Lucian found the bracers) to see if there are any doors secret or otherwise covered by the skulls. "Leave no... uh, skull unturned, I suppose..." (Perception)
If that search proves fruitless, he will suggest the party go back to where they were dropped in and go north from there (as opposed to east).
Assuming he finds nothing, which seems likely, and assuming the rest of the party would follow him, Buckthorn would trundle back to the hallway and then go north. He would proceed cautiously (Stealth) and keep an eye out for any traps (Perception again).
(Finally, a role above a 10!)