Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine your family member and obtain a history, I can not tell you what the exact cause of his symptoms is. However I will try to provide you with some useful information.
While there are many causes for achalasia and gastroparesis, from a neurologic perspective, a problem with the autonomic nervous system, which includes the vagus nerve but also many other components is a possibility. The autonomic nervous system is the part of the nervous system that controls blood pressure, heart rate, and other functions. It is not located in one specific part of the brain or other body part but is rather made up of several different components: a region in the brainstem, certain receptors located on blood vessels and in the heart, and small nerves in our skin, among other areas. Dysfunction of the autonomic nervous system due to whatever cause can lead to a variety of symptoms including but not limited to orthostasis (which means symptoms or signs resulting from assuming an upright posture), light-headedness with drops in blood pressure when sitting up or standing up (this is an example of orthostasis), syncope (passing out), constipation, diarrhea, sweating abnormalities, and gastroparesis etc. If there is a problem in the small nerve fibers, what is medically termed a small fiber neuropathy, in addition to these symptoms, burning/tingling in the feet and hands or mild sensory loss may also occur.
One of the most common causes of autonomic dysfunction, and of gastroparesis, is diabetes. Other causes of autonomic dysfunction include neuropathy, including large fiber and small fiber neuropathy due to diabetes, nutritional deficiencies, monoclonal proteinemias (conditions in which certain abnormal proteins are being produced), certain types of cancers can produce a paraneoplastic autonomic neuropathy etc. Certain types of parkinson's-type diseases and infections can lead to problems with GI motility as well. As you can see there are many causes, and each is diagnosed based on the history, examination, and some laboratory and/or other tests.
Treatment of gastroparesis due to autonomic dysfunction includes medications that improve the motility of the muscles of the stomach (such as metoclorpromide or erythromycin), and in some centers, a gastric pacemaker is being inserted in order to help the stomach contract though this is uncommonly done and only available in a few centers in the USA.
Continued follow-up with your gastroenterologist is recommended; with referral to a neurologist if your GI doctor suspects an underlying autonomic dysfunction.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.