Make optional rice cake balls (recipe below). Scoop out watermelon and honeydew with a melon-baller. Place them in a large bowl along with any juice from the fruits.
Add the ginger ale and the drinking vinegar to the fruits. Stir gently. Taste the drink and adjust acidity and/or sweetness by adding more drinking vinegar.
Optional rice cake balls
Mix the rice powder, sugar and salt in a bowl. Mix in the boiling hot water with a spoon. When cool enough to handle, knead by hand until a dough is formed.