This tunnel, which shows on your map as tunnel 4, opens when you pick up the bird tile from the platform on which the gold sarcophagus rests. There's not a lot here, but let's explore it all the same.
Hint 2
Go into the tunnel. Just past the two vulture statues, look to your left to see --
Hint 3
-- a modern-looking metal gate set in the wall, locked (naturally). How ... bizarre.
Hint 4
Keep going till you come to a closed door with a hand-shaped tile at one side.
Hint 5
Click on the hand tile to open the door, and you're now in tunnel 2. Turn left to get back to the main room.