Feel free to use your oil of choice; grape seed, safflower, or sunflower are oils that impart a less distinct flavor but they are highly processed; sesame and nut oils are less so, and produce a nice mayonnaise; a light olive oil is a great choice as well.Drizzle the oil in slowly so that the processor has time to fully emulsify the oil into the egg mixture. If the oil is separating from the mixture, you probably need to slow down the drizzle. You can store mayo in a sealed jar in the refrigerator for a few weeks.