Congrats on your very first MB troubleshooting and repair session!
Make sure you replace the failed bulb with the euro-spec model: The bulb sockets on those are nickel-coated...as opposed to the domestic gold-anodized counterparts you find at Walmart. Philips makes the nickel-coated type, as an example...you can find those in most auto parts stores.
Also, the taillight housing has the correct wattage requirements embossed near each bulb socket. The bulb failure indicator system is very sensitive to resistance, so using the improper bulb can cause false warnings from the system...