Eagles have a weak connection to the Season Avatars series. Eagles are the symbol of the Fip God of War and the royal Fip family. Lex, the War Avatar, swears by saying "Eagle's Claws" or "Eagle's Talons."
Since this series focuses on seasons, you would think equinoxes are important. They are; the Spring Avatar and Fall Avatar are always born on the spring and fall equinoxes respectively. However, Challens refer to both equinoxes and solstices as "soltranses." Each soltrans is marked by a special ceremony at the Four's Temple in Wistica. During each soltrans, the Avatars for the old and new seasons stage mock duels with fighting staffs. You can read about the fall soltrans in Fifth Season.