A brain stem tumor is a tumor in the part of the brain that connects to the spinal cord (the brain stem). A brain stem tumor is a tumor in the part of the brain that connects to the spinal cord (the brain stem). The symptoms of brain stem tumors vary greatly and can include ataxia, cranial nerve palsy, headaches, problems with speech and swallowing, hearing loss, weakness, hemiparesis, vision abnormalities, ptosis, and behavioral changes. Another possible symptom is vomiting. Headaches related to brainstem tumors may be worse shortly after waking up in the morning.