Patrick's Pocket Watch is a salvage item in the original Endless Ocean that is necessary to complete the main storyline. You find Patrick's Pocket Watch in the giant clam in Green Garden after you receive an email from Douglas Banner telling you that you might get a clue to unraveling Katherine's (Catherine's) past in Green Garden.
[To avoid spoilers, do not read beyond this point.]
After you find the watch and bring it to Katherine, she opens up to you and tells you about her father. He spent his life looking for the Ancient Mother, and as a part of his quest, he went searching for clues in Green Garden and "never came back". This suggests that Patrick Sunday became entangled in the dangerous fronds of kelp and was unable to escape, thus drowning and perhaps spawning Katherine's fear of water. This ties into the event later in the story where the player almost meets the same fate: while diving to Green Garden on a story mission, you become entangled in several kelp fronds and have to call your dolphin partners to help get you out. Katherine only reveals her father's demise after this event, lending some reason to her panic.