The gaze point data of the individual eyes are available through the Gaze SDK. But even with that I’m not sure it would be possible to do what you want to do.
When a calibration is being done, the eye tracker calibrates per eye, based on the assumption that the eye-gaze of that eye is actually pointing toward a predefined point on the screen. When a person with strabismus is calibrated, only one eye can be assumed to point toward the predefined point. The other eye may be pointing somewhere else, so the calibration for that eye may be loaded with incorrect values that would lead to unpredictable offsets in the calculated gaze point for that eye. In the case of alternating strabismus, this would be even more unpredictable, since different eyes could be used for focusing different points during the calibration process, and no consistent calibration would be obtained for any single eye.
One alternative could be to use the default built-in calibration of the eye tracker instead. This would not give a good accuracy of the gaze point, but since it would use consistent calibrations for each eye, offsets should be quite consistent over the screen.
So, the question is whether the gaze point data from the individual eyes, given these problems getting a good calibration, will be correct enough to be able to decide which eye’s data to use.