Accessing visual information is crucial yet challenging for people with low vision due to visual conditions like low visual acuity and limited visual fields. However, unlike blind people, low vision people have and prefer using their functional vision in daily tasks. Gaze patterns thus become an important indicator to uncover their visual challenges and intents, inspiring more adaptive visual support. We seek to deeply understand low vision users' gaze behaviors in different image-viewing tasks, characterizing typical visual intents and the unique gaze patterns exhibited by people with different low vision conditions. We conducted a retrospective think-aloud study using eye tracking with 20 low vision participants and 20 sighted controls. Participants completed various image-viewing tasks and watched the playback of their gaze trajectories to reflect on their visual experiences. Based on the study, we derived a visual intent taxonomy with five visual intents characterized by participants' gaze behaviors. We demonstrated the difference between low vision and sighted participants' gaze behaviors and how visual ability affected low vision participants' gaze patterns across visual intents. Our findings underscore the importance of combining visual ability information, visual context, and eye tracking data in visual intent recognition, setting up a foundation for intent-aware assistive technologies for low vision people.