Hi, I am Gastro surgeon Dr. Satish Devakumar, Gaging & Saliva coming out is a normal reflex phenomena when you throat is stimulated or may be Gastro Esophageal Reflux Disease. Kindly follow these suggestions : 1. Avoid heavy meals at night. 2. Restrict your tooth brushing time to less than 2 minutes. 3. Do saline water gargling. 4  restrict oily & fried foods. 5. Use additional pillows to raise your head height. 6. Avoid carbonated drinks,  Sweet,  tea & coffee. If you still continue to have same problem, consult your doctor for further assistance.

Morning vomiting could be due to gastritis ,do you have GERD ? It can also be normal physiology , with the gag some amount of saliva ,don't stimulate posterior part of tongue as it causes gag reflex .