Have the watch stop and your pulse stop at the same time. Could lead into it having the spec use your watch or their borrowed watch to take your pulse as any nurse/doctor would do using the second hand. As the watch comes to a stop so does your pulse, then both begin again. Play it off as you exist in an alternate reality and the ability to make them believe their time has slowed and come to a stop, while your time continues to tick, thus keeping you alive (stopping a pulse would kill most people in reality).
Might be a bit over the top and muddled to have both happening at the same time but I am almost certain there is a method to pull them both off at the same time, perhaps not impromptu but nevertheless still possible.
Just random thoughts from the far side...