In a small bowl, combine 1/2 cup of the mayonnaise, 1 Tbsp. of the vinegar, 1 tsp. of the garlic, orange zest, and a dash of pepper. Set aside.
In a medium bowl, combine onions, egg, 3/4 cup panko, 1/4 tsp. pepper, and remaining mayonnaise, seasoned rice vinegar, and garlic; mix well. Add tuna; mix well, breaking up large chunks.
Form into 12 patties about 2½ inches in diameter and 1/2 inch thick. Sprinkle about 1/2 tsp. panko crumbs over both sides of patties. In a heavy 10-inch skillet, melt 1 to 2 Tbsp. of the butter as needed over low to medium low heat. Cook half of the cakes at a time, without turning until nicely browned, 3 to 4 minutes. Watch carefully to avoid overbrowning. Gently turn cakes with a spatula. Cook until cakes are set and bottoms are golden brown, 3 to 4 minutes. Serve with mayonnaise sauce.