Remove pits from peaches and mash in a medium-sized bowl. Add sugar and ginger, stir well. Cover and refrigerate overnight.
Press peach mixture through a fine-mesh sieve into a clean medium-sized bowl. Discard peach solids. Add both vinegars to peach juices. Whisk to combine. Pour through funnel into clean bottle. Seal bottle and shake vigorously. Store in refrigerator for 3 to 5 days, shaking periodically to help dissolve sugar. Once sugar has dissolved, serve with seltzer or white rum. Shrub can be stored for several months in refrigerator.
