Combine the light mayonnaise, ketchup, sweet pickle relish, yellow mustard, white vinegar, paprika, onion powder, and garlic powder in a small bowl. Stir well, cover, and refrigerate to allow flavors to meld.
In another bowl, gently combine the ground beef with salt, black pepper, and garlic powder. Mix just enough to combine, then divide the seasoned beef into 8 equal, small portions.
Lay your small flour tortillas flat on a clean surface. Take one portion of the seasoned beef and press it thinly onto one side of each tortilla, spreading it right to the edges.
Heat 1 tablespoon of vegetable oil (or olive oil) in a large skillet or cast iron pan over medium heat until it shimmers. Carefully place a few tacos (don't overcrowd the pan!) into the hot skillet, beef-side down. Cook for 4-5 minutes, gently pressing down with a spatula, until the beef is fully cooked, deeply browned, and wonderfully crispy.
Flip the tacos so the tortilla side is now down. Generously sprinkle shredded cheddar cheese over the cooked beef on each taco. Continue to cook for another 2-3 minutes, until the tortilla turns golden and crisp, and the cheese is perfectly melted and bubbly.
Carefully remove the finished tacos from the skillet. If you have more tacos to cook, add the remaining 1 tablespoon of oil as needed and repeat the cooking process. Finally, load up each warm taco with fresh shredded lettuce, diced tomatoes, and sliced green onions. Finish with a generous drizzle of your prepared Big Mac-style sauce and serve right away for maximum deliciousness!