My brake lights on my C300 stay on for approximately 24 hours after a car wash.

Can only guess here -- if your dealership has already performed troubleshooting and replaced components, it's really best to ask them to check their work and recheck it! Or, obtain a third party opinion from another technician near you.

I had the same problem on my 2009 C300. After a good rain or a car wash, my brake lights would stay on until the next day. It did it for years until I had to figure it out. I traced it back to the rear fuse box in the trunk. It was getting wet. I do not know how many years they did this, but if you open the trunk and go around the sealing edge of the trunk, you will see plastic molding with plastic body clips holding it in place. The body clips are specially coated with a rubber seal to stop the water, but mine were dry rotted and was letting water go straight through. I replaced them and haven't had the problem since.