In a food processor or blender (or use an immersion blender), combine the eggs, egg yolks, mustard, lime zest and juice, lemon zest and juice, and salt and pepper. With the machine running, slowly add the oil in a thin steady stream until the mixture is emulsified and thickened and all the oil has been incorporated. Taste and adjust seasoning with more salt, pepper, or citrus if desired. Can be made ahead of time; will keep refrigerated for up to 3 days.