Sorry, you misunderstood.
By 'move timer' I am referring to a timer that counts up from 0:00 at the beginning of each turn during a game. Once a player completes his move a new count from 0:00 begins on the opponent etc. etc. If this timer reaches 10:00 there can be no question that the player has timed-out.
It is more efficient than the Eliters Timer Clock that you describe, as it begins from the instant that the player is requried to make their next move in the game. Under your method, there will be a delay of some length before it is noticed that the player is idle. Then more delay while the TD's attention is sought, they are informed of the problem and actually click on the eliters timer to start it. While all the above is going on, none of the 10 minutes is being used up and the more tourneys you have going and the more players requiring timers, the greater these delays will inevitably be.
Clearly the move timer doesn't work for all situations, like for players who go missing between rounds, for example; it does require that a game has actually been started. In this case, however, it is the fairest method and should be used.