Brake lights are stuck on all the time. 320 2002 Mercedes

Are the brake lights stuck on or are you just seeing the parking lights on without the brake lights lighting up? Sounds like you have no rear brake lights, check your emergency light switch. Sometimes it may not switch completely, turn it on and off a few time and then recheck it.

While I'm not overly familiar with Mercedes, I'd assume that it still has a brake light switch located on the bar of the brake pedal itself. This switch is typically just a "plunger" style switch, where when you push the pedal down as if applying the brakes, the plunger extends outward turning the brake lights on. When the pedal is released, as if letting off the brakes, the plunger is depressed causing the lights to shut off. If that plunger gets stuck in a depressed position, the lights will remain off at all times. Check that first, along with the brake light fuse and/or relay. Good luck.

Then your BRAKE SWITCH IS BROKE or has fallen off the Brake Pedal

It might be a failing break light switch which is very common to cause this complaint, you can try pressing very hard on the brake pedal when selecting drive - if it selects drive after doing that you need a new brake light switch, If not it could be your shifter module thats at fault - we sometimes see that fail aswell.

If you mean that the brakes are hard to push but the pedal still only travels its normal distance then:
This is either a brake assist valve. A brake booster problem, or the vacuum line that feeds the brake booster.

If you mean it goes way to the floor before it stops you then you have a bad master cylinder or some air in a line.

I'll assume you don't have any warning lights on.

It is not normal. I would say your break switch is sticking. There is a button on the end that sometimes gets stuck. It turns your brake lights on and off.

Check your fuses according to your manual. Sometimes European models the breaking ligth system work in a parallel circuit it means if one light bulb goes off the other one will fallow.

Change your light bulbs (both)

It will come on sometimes while driving in certain conditions, like a rough or loose road surface. It's indicating that the stability and antilock brake systems etc are in operation while those road conditions exist.

It will go out when normal road conditions are detected.

check and make sure the brake light are working, the brake light circuit must be activated to release the safety park interlock system, this system uses a solenoid, if the brake lights do work then the solenoid may be bad or the pin is stuck in the shifter.

Try checking the brake light sending unit. Are your brake lights even working. Many newer vehincles will not shift out of park unless the brake pedal is depressed. However, a faulty sendind unit located on the pedal itself can keep you from moving anywhere. Just check to see if your brake lights are working to know if the sending unit is working.