I don't understand your logic behind the statement: "Since the light is stated to only be on for 6 seconds after ignition is turned on, I do not think it is the bulb"
What does when it comes on have to do with whether it is the reason it doesn't. The main reason all the lights come on in the key on engine off senario is to do a bulb and systems check. By putting the car KOEO (key on eng off) one can view the systems with warnings and determine if the warning bulb is OK on systems known to exist.
The other day we worked on a ABS problem, untill we noticed that every time the control unit was removed the windshield washer fluid light came on. Someone had reversed the bulbs in their slots and the real problem was the washer was out of fluid.
Bosch Master, ASE Master, L1
33 years MB technician