Hello and thanks for your question.
Please allow me to ask a few questions to better understand the situation.
Did/does your brother wear contact lenses or glasses and if so, do these lenses help him see any better?
What was the mechanism of action of the trauma? What was he hit by, how fast was it going? Did he lose consciousness with this accident?
Does he have a history of migraine headaches?
Can you give me a more precise level of vision in the right eye? Can he count fingers, see hand motions, can he only see light or not at all, or can he see the big E on the chart or better?
So is there times when he can see well / close to normal out of the right eye (the non-traumatized eye)? In other words, does the vision fluctuate enough that he can see more than just a bright dot out of the right, untraumatized eye?
What level of vision does he have in his left eye (the traumatized eye)? count fingers? hand motion only? perceiving light only? or is it better?
Assuming there was no trauma to his right eye, then there are very few things, if any, that could be causing blindness in the right eye. Rarely, facial/orbital trauma can cause trauma to blood vessels in an area called the cavernous sinus, which has blood vessel connections to the both eyes. This may cause a carotid-cavernous fistula (CCF for short). In this case, however, there are usually at least some signs to suggest something pathological happening in the non-traumatized eye; however, these signs can be subtle and a CT scan may not pick up this type of problem. This seems less likely however.
I would say that it is not normal that your brother is unable to sign his name when the paper is put directly in front of him and does not coincide with vision loss in his right eye.
Other than that I do not have any possible explanations for vision loss in his right eye. A consultation with a neuro-ophthalmologist might be the best thing for your brother.
Does this address your concerns?
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Disclaimer: My opinion is solely informative and does not constitute an informed medical opinion or recommendation. For an informed medical opinion and/or recommendation you must see an eye doctor.
As far as the vision loss in the untraumatized eye, migraines can cause intermittent vision loss, but likely not the degree of vision loss you are referring to.
A traumatic brain injury is unlikely to cause a unilateral vision loss (vision loss in the untraumatized eye). The eye that was traumatized may be permanenatly damaged from a traumatic optic neuropathy, which, if that is the case, means his prognosis for useful vision in that eye is poor.
It is still clear to me why he has vision loss in the untraumatized eye, but for his brain to be the cause of it, he would need a much more significant overall brain injury and it would not cause cyclical vision changes.