Final answer:
The lesion suggested by the symptom of total paralysis with preserved vertical eye movements is likely located in the brainstem (pons or midbrain) and could indicate locked-in syndrome.
Step-by-step explanation:
The question involves determining the site of a neurological lesion based on the symptom of total paralysis except for vertical eye movements. This type of presentation suggests damage to the part of the brainstem known as the pons or midbrain, specifically affecting structures responsible for horizontal gaze such as the paramedian pontine reticular formation (PPRF) or damage to the nerves controlling eye movement, sparing the structures that enable vertical movement.
This condition may be referred to as locked-in syndrome, which is characterized by near-total paralysis, where patients retain consciousness and the ability to perform vertical eye movements, often as a result of a stroke, trauma, or other brain injury. Testing for conjugate eye movement, such as in cases of internuclear ophthalmoplegia, would show whether there is proper function of the related nuclei and the medial longitudinal fasciculus (MLF). However, the original question does not point to this information but describes a condition consistent with a lesion in the brainstem.