If it is the third brake light the warning light should only come on when you apply the brakes. The system is only supposed to tell you a light is not working when you try to turn that light on (when you operate the brake). There are small marker lights at each rear corner that should be on whenever you turn the headlights on. It is difficult to see these lights are even on when the sun is out. Check those out too.
1995 E420 - retired
1986 420SEL - retired