How do you get the glowing amulet?
Choose the find another way in on the Bridge screen, you should pick up the 5 Glowshrooms after donig that or after you look around on that cave screen, talk to either the lizardess inside the inner temple in the ruins about it or the Witch in her Hut inside the swamp to get the item needed for it, after you say yes to having her create it, equip it before going back to the cave and you can explore it, you need to keep that item equiped if you want to continue exploring the place each time you go underground.