Off of the dark, rainy node, the one with the owl's head that follows you. The map marks a secret on this node, and a grayed-out child node. Are they two different secrets?
3 Answers
There are two "secrets": the four owl puzzle (denoted by a question mark on the node), and the subsequent anticube room.
Four owls
In four places, an owl appears at night. Speak with each one:
in the waterfall level near the pillar (green tree, first warp zone),
in the windmill level near the windmill (orange tree, air warp zone),
in the forest near the transforming cabin (green tree, outside rainy warp zone),
and outside the octopus-looking building containing the revolving model of the solar system and the counting cube (pink tree, temple/science warp zone).
These locations were shown on the walls of the fez-wearing elder's house (in Gomez's hometown, across the bridge).
Hidden room
After speaking with each owl, they fly to the rainy warp zone's giant owl room. When all four arrive, a panel reveals a door behind the owl statue opposite the entrance. It leads to another owl room with an anticube.
Glitch: If you remove the patch, the original version of the game had a glitch where you could access the hidden room without the four owls: stand in front of the entrance, rotate the room twice, and press up to enter. Keep in mind, the room won't be "completed" until the main secret (four owls) is finished and the next room is visited.
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I just got it by accident. Stand in front of the door below the owl but don't press up. Now, Spin the screen so you're standing BEHIND the owl. Now press up to go through the door even though the door isn't facing the screen. Hope that helps.
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Probably a bug or glitch that's been fixed. It doesn't work on the PS3/PS4/PSV version.– NolonarCommented Mar 31, 2014 at 16:33
There are four live owls within other nodes that you need to talk to in order to open this door. You can find clues to their locations in the village in the house of the guy with the eye patch. I think they only appear at night.