The direction of gaze deviation can be an important physical exam clue.
In a healthy person the ability to look side-to-side is controlled by a part of the brain called the Frontal Eye Fields (FEF). The right hemisphere FEF’s drive the eyes to the left, and the left hemisphere FEF’s drive the eyes to the right, following the normal pattern of cortical motor control.

Strokes or other destructive lesions involving the FEF’s cause a gaze deviation that “looks towards the lesion.” This is because the intact FEF is now working unopposed to drive the eyes towards the non-functional side. Gaze deviation towards the lesion is therefore expected, and is called “right way eyes.”
So, what are “wrong way eyes?” When there is a lesion, most commonly a focal seizure, causing increased activity in one FEF, it actually drives the eyes away from the lesion – the opposite of what you expect with “right way eyes.” So, if a patient presents with a left frontal lobe injury, but his eyes look like those in the portrait of Martin Luther above (ie, an apparent right gaze deviation), you would suspect an activating lesion such as seizure.
Caveat: Seizures cause wrong way eyes by increasing activity in the involved FEF, but in the post-ictal state, the patient may then develop right way eyes.