Honestly it's stupid we can not erase what we previously posted, CORRECTION the teleport of the digsite area only come with 2 teleport destinations in total , one is the digsite and after you can convert it to teleport you to fossil Island directly
Also, the necklace comes with 3 teleport options, once discovering the abandoned castle on fossil Island you can convert The amulet to teleport you specifically to the abandoned castle on the island other than that it only has three options for a teleport
Well the wiki says that giving the guy on the second floor the information about the quest Curse of the Empty Lord, then he will grant you a lamp for 10k xp