Oil a cookie sheet with olive oil. In a medium bowl, lightly beat eggs with a wire whisk. Whisk in the ketchup, mayonnaise, butter, seasoned salt, and paprika. Stir in the pimentos and chives. Add lobster meat and 1/2 cup of the crushed butter crackers. Stir gently to combine. Form the mixture into 8 cakes, using a 1/3-cup measure for each. Dredge both sides of the cakes in the remaining 1/2 cup of cracker crumbs and place on oiled cookie sheet. Flatten slightly to make a 3-inch cake. Bake for 8 minutes, carefully turn each cake, and continue baking for another 8 minutes.
Drizzle Rosey Sauce over cakes or serve on the side.
Combine all ingredients in a small bowl and stir until smooth.