Is it common for strabismus to switch eyes?

Yes, strabismus can alternate between the eyes, especially when the vision is similar in each eye. This can also change if the visual acuity (sharpness) is improved in the deviating eye with patching treatment. In that treatment, the dominant eye is covered to cause the crossing eye to see better.  As the vision improves, that eye may stay aligned and the previously dominant eye crosses.

Other factors can also contribute to which eye wanders, such as changes in glasses prescription, loss of vision from other eye diseases, and rare neurological conditions.