It can be accessed through the far left side of the Underground Misty Cave regardless of route choice. In the Light path, it can also be accessed through the green Teleportation Magic Circle at the Spring of Revgato.
Underground Misty Cave (Chapter 1):
After defeating the Lizardians in the Underground Misty Cave who attacked Adrian a second time, Eirudy has to chase after him yet again when he runs deeper into the cave. Enter the Spring of Revgato - Root. Once she approaches the center of the room, she will run into Raymond, the captain of the Lizardians. When Raymond instigates a fight, Lize intervenes on behalf of Eirudy, and the two fight off Raymond together.
Once Raymond and Lize both leave, Eirudy resumes her search for Adrian. Go towards the back of the room, and she will eventually fall unconscious. She will awaken at the Spring of Revgato.
Inside the Spring of Revgato (Chapter 4, Light/True Paths):
After seeing a vision at the Temple of Marii, Eirudy will decide to visit the Spring of Revgato (though what they really mean is the Spring of Revgato - Root). In the True path, this will happen right after visiting the Temple of Marii. In the Light path, Eirudy will first head to Shubeth Village to rescue Adrian, and will go to the Spring after several cutscenes.
At the Root, she finds Raymond and will fight him again. Once she defeats him, Lize appears again to reprimand Raymond, who then vanishes. Lize tells Eirudy to visit the spring in the Eastern Misty Forest to find out more about herself.