What is the symbolism of the gold watch?

I think it functions as a symbol in the sub plot about loyalty, friendship and being a 'true man'.

He gets it from the Captain with explanations about what the Captain and his father went through, the ordeals and humiliations which were suffered to connect with Butch via this watch. Remember that Captain says that "when two men are in a situation like that they take on certain responsibilities for each other"

The rescue operations where Butch gets his gold watch back and when Wallace and Butch are captured in some ways parallel military rescue mission.

However, the most important aspect was when Butch had escaped the basement but knew he could not abandon Wallace to be raped and tortured, like his father and the Captain he knew he had taken on a responsibility for Wallace.

In the basement Wallace is being raped. There seems to be foreshadowing with references by Wallace to asses ("pop a cap in his ass" etc.) and the watch being concealed in Butch's father's and then the Captains rectum.

Butch risks being recaptured to free Wallace.

Perhaps this rescue mission to Wallace was a way for Butch to connect with his father and gain some closure? Symbolically he might be rescuing his father from the torture of the POW camp.

Is the watch really "symbolic"? I think its role is much more direct: the watch is simply the central plot device in the Butch-related parts of the movie.

The watch is Butch's prized possession, a token his ancestors went to great lengths to pass on to him -- as Tarantino chose to explain in the movie's very first scene. To Butch, the watch is loaded with sentimental value.

Butch's attachment to the watch causes him to go back to his apartment, leading to his confrontations with Vincent Vega and then Marcellus Wallace, which make up the main action of the movie. Any other possession would not have been worth risking all that trouble.