How does the story of Hanukkah appear in the Gospel of John?

In the Gospel of John (10:22), Hanukkah is mentioned briefly as the Feast of Dedication, or enkainia in Greek. The text describes Jesus entering the Temple of Jerusalem during the winter festival.1

As the narrative unfolds, the assembled Jewish people ask Jesus whether he is the messiah. When he claims to be the son of God, they reject his assertion, attempt to arrest him, and take up stones, which ultimately forces him to flee the scene.1