Pour lime juice, vinegar, salt, and sugar into a medium bowl. Set a strainer over bowl. Finely shred ginger, put in strainer, and press out juice into bowl. Whisk brine to mix.
Slice jicama 1/4 in. thick and cut slices in halves or quarters. Slice peppers and chile into thin rounds. Add to brine and turn gently to mix.
Chill at least 1 hour, stirring every now and then so flavors can develop. Serve cold. Keeps, chilled, up to 2 days.
Note: Nutritional analysis is per 1/4-cup serving.