Heat oil in heavy medium saucepan over medium-low heat. Add onions and sage. Cover and cook until onions are deep golden brown, stirring occasionally, about 20 minutes. Remove from heat and let cool.
Whisk together mayonnaise and sour cream in a medium bowl to blend. Stir in the cooled caramelized onions, salt, and pepper. Cover dip and refrigerate until flavors blend, about 2 hours.