Heat a cast-iron skillet or heavy stainless steel pan over high heat until smoking.
Press 1/4 cup of ground beef into each tortilla, spreading to edges to form a thin patty.
Sear patties for 1-2 minutes on each side until crispy and browned.
Top each patty with a slice of American cheese and cover pan to melt cheese, 30 seconds.
Flip finished patties to reserved tortillas.
Prepare sauce by combining sweet relish, vinegar, ketchup, sugar, mustard, garlic powder, onion powder, salt, pepper, and paprika. Mix well.
Spread 1 tsp sauce on each half of the taco shell.
Add 3-4 pickle slices per taco.
Sprinkle diced white onion over the patties.
Fry tacos in pan for another minute per side until warmed through.
Serve immediately with additional sauce on the side.