Once they kill themselves head up to them and examine them.
They'll each hold a special type of egg. 1 scarlet and 1 rust colored egg.
Head for the doors and they'll be locked. Open your inventory and use one egg on each door. It doesn't matter which egg you place on which.
Once you place both eggs into the sockets of the door they'll unlock and you'll be able to pass through. It doesn't matter which door you use to enter.
Head for the only open door in the area.
Beyond the door there's a long hallway and a conversation can be heard through the walls. Listening to this conversation will affect your ending. Running past the corridor and not finishing the conversation will also affect the ending you'll receive.
Enter through the door at the end of the hallway to get to our final destination.
Turn towards James's left and start climbing up the staircase. Keep climbing until you get to the highest floor and a cutscene will begin to play.