In a small stainless steel saucepan, combine vinegar, soy sauce, fish sauce, maple syrup, onion, and garlic. Bring to a boil over medium-high heat, stirring occasionally to ensure maple syrup is fully incorporated into the brine. Remove from heat.
Meanwhile, pack hot chiles, mild chiles, and chayote into a heatproof, non-reactive, 2-quart container, such as a glass canning jar or Cambro container. Pour hot brine over vegetables to cover. Cover surface of brine with piece of plastic wrap or parchment paper, then place a weight on top to keep vegetables submerged. Let cool to room temperature, about 1 hour. Cover with a tight-fitting lid, and refrigerate for at least 24 hours before serving. Pickles can be refrigerated for up to 1 month.
