Both rear brake lights don't work, the third upper brake light does. Dash warning light illuminates to say brakes lights are out.

Do you mean the brake lights on the rear of the vehicle or the brake light on the dash?

I can almost 100% guaranty the turn signal switch is the problem. Power for the brake lights starts at the brake switch. power then splits from there and the third brake light gets power directly from the brake switch. Since the turn signal and the brake lights are on the same bulb power for the brake lights is routed through the turn signal switch. the switch depending on what position it is in will allow brake power or turn signal power to there respective left or right brake/turn bulbs.

If you hold your foot on the brake pedal and wiggle the turn signal and or play with the hazard switch the brake lights will almost always intermittently start to work. this will confirm a bad turn signal switch which is pretty common on GM vehicle with this style setup.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

Hi. Thanks for your question. For issues related to brake warning lights on dash illuminated for Mercedes C180, 1996 saloon. You can visit https://www.reliable-store.com and download the entire workshop manual which includes all the information along with the diagrams for better understanding. Good day!

your brake lights are connected to a button that is adjustable on the upper end of the brake pedal, under the dash. check and adjust the button so it is only activated when the brake is pressed.

Study light? Do you mean warning light?
There are sensors clipped into the brake pads on the front left and rear right wheels. When the brake pads get very thin, those sensors rub on the brake rotors, and the light illuminates in the dash indicating that it is time to replace the brake pads.
The light can also illuminate if something damages the wire to the sensor. I usually replace my pads before they get down to the sensors, so I re-use my old sensors. Although the wires are fairly well secured to the suspension, after a few years, the wires can get chaffed from the wind blowing them around, and the damaged wire can turn on the warning light.

LH/RH lights cable could be disconnected anywhere, will take a long time to trace.
Center Brake Light and LH & RH should be connected at one point.
Jump a cable from Center Brake Light to one of Rear Break Light.
Hope this will works.

first get a auto repair manual for you car at the local auto parts store or Ebay, then check the manual for dash light location and rear light locations , next with a continuity checker check for gound and power in the sockets , may be a bulb got over heated and shorted a wire causing dash and rear lights not to work

Turn signal switch.

My 2001 S60 just had the same issue. The "check brake light" error message on the dash and the brake lights not illuminating ( the upper center glass brake light would). I found that both bulbs had failed which I replaced. The fuse was okay but still the error message was found on the dash when the brake peddle was pressed. I purchasing a dealer $30.00 brake light relay and the problem is fixed. However, there isn't a diagram anywhere that shows which relay was for the brake light relay. In my 2001 S60, the relay is in the trunk, beneath the driver side removable upholstered cover. The relay panel has ~ 10ea of the same relays and a few other odd sizes. There is a vertical column of relays on the left and right. I found the brake light relay is located between two other relays on the upper right column. It was difficult to reach due to a larger relay on it’s right.

depending on the system if it is 2 channel or 4 channel one of the sensors that are located on the backing plate located behind calipers is eithier faulty or dirty you can try brake cleaner these sensors use a small magnet pickup device to sense when the wheel "locks up"