The Gemara does not provide a working Halachic definition of a Goses. What it does tell us, though, is the difference between a sick person and a Goses. The Gemara in Kiddushin (71a) says that most sick people survive and most Gosesim die. This would suggest the following definition of Goses: someone that will probably not survive despite medical intervention. This being the case, the type of medical condition that constitutes Gesisah has probably changed over the years with advances in emergency medicine.

Rav Moshe Feinstein (Igros Moshe, CM 2:73) says that the doctors don't know the signs of Gesisah because it is not important to them (they don't consider moving a Goses to be Retzichah), but he doesn't tell us what they are either, he just says that the signs are well known to the Chevros Kadisha that deal with this issue all the time.

Rav Moshe Sternbuch (Teshuvos v'Hanhagos, 1:872) says that the signs of Gesisah are when the person's breathing becomes heavy and the blood pressure drops significantly.

Rav Shlomo Zalman Auerbach says that someone who is hooked up to a life support system is certainly at least a Goses (Safek Goses Safek Meis) and therefore it is forbidden to do any tests on him - to determine whether he meets the criteria of brain death - if the tests involve moving him or injecting material into him (which Rav Auerbach considers more severe than moving him) because these tests are not done for the benefit of the patient.

Kol Tuv,

Yonasan Sigler