Vision contributes a lot to balance. The vestibular therapist should check you for eyes open and eyes closed balance. If your eyes closed balance is close to normal but your eyes open balance is poor, it suggests you need to get the vision issue resolved. A behavioral optometrist can be helpful.
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Neuro-ophthalmologists do not have a good track record based on posts on NT. But, every neuro-ophthalmologist is different.
You could start your exam with the VT by asking, Is my balance problem mostly caused by a vision problem ?