Place the shaved red onion and the thyme sprigs in a small glass or non-reactive container. Combine the rice wine vinegar, sugar, and the reserved pear peelings and seeds in a small saucepan. Bring mixture to a boil. Strain liquid into the container holding the onions and thyme sprigs. Discard the pear peelings and seeds. Allow pickled onions to cool to room temperature and then refrigerate until cold.

Right before serving, strain the onions, reserving about 2 tablespoons of the pickling liquid. Discard the thyme sprigs and toss the pickled onions with the julienned pears, watercress, salt, pepper, and the 2 tablespoons of pickling liquid. Serve immediately.