In normal ICAO operations a flight is flown as filed or as cleared. Controllers than expect the flight to appear on their screen squawking the proper code, and contacting or answering up on the correct freq. Where the flight crosses many airspace divisions, the controllers hand off to the next guy for flight following.
Yes, I know.
So the best place to change course in order to confuse the Controllers for the longest period of time, would be right between airspace divisions, or right before passing into a new division. Would that make sense?
From what I gather, the flight stopped transponding 1 minute before the pass off to the Vietnamese controllers was supposed to happen.