The most common cause of vertical gaze palsy is damage to the top part of the brain stem (midbrain), usually by a stroke or tumor. In upward vertical gaze palsies, the pupils may be dilated. When people with this palsy look up, they have nystagmus. [merckmanuals.com]

They may also have nystagmus. (Nystagmus is involuntary, repetitive fluttering movements of an eye in one direction, then slow drifting of the eye in the other direction.) [merckmanuals.com]

Palsies can also be caused by damage to the front part of the cerebrum, usually by a stroke. The resulting palsy may not be as severe as that caused by damage to the brain stem, and symptoms often lessen with time. [merckmanuals.com]