How do stars located near the celestial equator appear to move across the sky from a Northern Hemisphere perspective?

They appear to rise due east and set due west, traveling in great circles.

The apparent movement of stars is directly correlated with their proximity to the north celestial pole. Stars that are very far from the pole, such as those near the celestial equator, trace the largest possible paths across the sky relative to the observer. Since the celestial equator is a projection of the Earth's equator onto the sphere, stars near it appear to rise almost exactly due east and set almost exactly due west. This motion follows a great circle path across the observer's sky because they are farthest from the pivot point defined by the Earth's axis extension.