This is a follow-up question to How likely would Abraham Lincoln be to survive his wounds today?
You don't have to see a CT scan or autopsy to know if the brainstem is injured (directly or indirectly), if it doesn't work right.
The description of the first doc at the scene mentioned that Lincoln was not breathing, and one pupil was dilated (the latter a clear and unequivocal sign of dysfunction of the third cranial nerve or the upper brainstem, from where it comes). Unfortunately, the second doc described the enlarged pupil being the right one (it's extremely unlikely to have been one and then the other - one of the doc's was probably mistaken as to the side).
By 3 hours after injury, both pupils were fixed and dilated, and Lincoln showed extensor (decerebrate) posturing - again, all signs of profound brainstem dysfunction (but not yet brain death, though pretty close to it).
Now, what is decerebrate posturing? See http://en.wikipedia.org/wiki/Abnormal_posturing#Decerebrate
Decerebrate posturing is also called decerebrate response, decerebrate rigidity, or extensor posturing. It describes the involuntary extension of the upper extremities in response to external stimuli. In decerebrate posturing, the head is arched back, the arms are extended by the sides, and the legs are extended. A hallmark of decerebrate posturing is extended elbows. The arms and legs are extended and rotated internally. The patient is rigid, with the teeth clenched. The signs can be on just one or the other side of the body or on both sides, and it may be just in the arms and may be intermittent.
A person displaying decerebrate posturing in response to pain gets a score of two in the motor section of the Glasgow Coma Scale (for adults) and the Pediatric Glasgow Coma Scale (for infants). Decerebrate posturing indicates brain stem damage, specifically damage below the level of the red nucleus (e.g. mid-collicular lesion). It is exhibited by people with lesions or compression in the midbrain and lesions in the cerebellum