Just a nit pick here, the Golden Pocketwatch fires off of the Free Triggered Ability icon, those can only be used during a player window, none of which is at the start or end of any phase.
That being said, the Reaction Triggered ability could have a trigger off of a start or end of phase. Am I missing something? Did FFG use the wrong symbol? I get the intent of the card, but seems like the way its worded, it can't be used by a strict reading of the rules.