Will chewing gum always help with ear pressure in long flights or is there a better non-medication method?

Valsalva. Try performing a valsalva maneuver - pinch your nose and gently "blow" air out of your nose while at the same time bearing down like you are lifting something. This will force air up your eustachian tube and expand the middle ear and prevent traction on the ear drum which is what causes the pain and fullness during descent.
Yawning. Chewing gum equalizes the pressure in the nasopharanx and sinus. By opening up the eustacean tube, a valve that runs from the middle ear. Chewing gum, yawning, opening and closing your mouth and swallowing hard are ways of flexing that tube to physically open it. On the drug side, take an over-the-counter decongestant an hour before their flight also helps.
Chewing gum helps. Any action that will help open your eustachian tubes and equalize the outer ear pressure and inner ear pressure works. Some of these actions are: chewing gum, yawning, opening wide, swallowing, etc. Over time you will find a method or movement hat works best for you. You can find more information under eustachian tube in wikipedia.