Beat the eggs and buttermilk together in a mixing bowl until smooth. Mix in the chicken wings, cover, and refrigerate 30 minutes. Combine the flour and crushed crackers with the pepper, thyme, cayenne pepper, salt, and garlic powder in a large mixing bowl.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
Remove the chicken wings from the buttermilk marinade, and discard the remaining marinade. Allow the excess buttermilk to drip from the wings, then press into the bread crumbs to coat.
Cook in batches in the preheated deep-fryer until the breading is golden brown on the outside, and the chicken wings are no longer pink at the bone, about 10 minutes per batch. Drain on a paper towel-lined plate, and season to taste with salt before serving.