In a non-reactive bowl, combine the squash and salt, toss to coat, and allow to stand at room temperature for about 4 hours. Drain, rinse well, and squeeze out extra moisture by the handfuls.
In a medium non-reactive pot, combine all remaining ingredients and bring to a boil over medium-high heat, stirring once or twice to dissolve the brown sugar. Add the squash, bring back just to a simmer, then remove from the heat and allow to cool to room temperature, uncovered.
When the mixture has cooled to room temperature, cover and refrigerate.
The squash will be tasty in about 2 hours, but will improve in flavor if allowed to sit overnight. This pickle will keep, covered and refrigerated, for about 2 months.
Recipe courtesy of Quick Pickles: Easy Recipes with Big Flavor, Chronicle Books, 2001