Had that same problem on my 300E, except the bulbs worked fine...the dash light came on solid during the day (headlights off) and would be okay with the headlights on.

I found that one of the metal strips on the RIGHT side (in my case) had a connection problem...I took a needlenose and twisted it into shape until it stopped giving off the false indicator.

It ended up being a non-issue when I backed into a truck and cracked the taillight lens...bought a complete assembly so the problem disappeared for good!

Make sure the bulbs you use are the correct wattage...usually embossed on the housing next to each bulb receptacle.

__________________
2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car