Right passenger brake light doesn't work but parking light and turn signal does. Is the bulb bad?

Check the bulbs with a test meter, or swap left to right and right to left. Check connectors and wiring and in particular grounding connection on that side of the MYSTERY vehicle!

'year make model' in all questions please.

https://www.google.com/search?q=Right+Brake+light+and+right+turn+signal+doesn%27t+work

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I have to think the problem is inside the turn signal switch, a poor internal connection. You know the brake signal first goes through the turn switch before it goes to the bulbs. That is why the brake lights and rear turn signal lights share the same filament in the bulb, and the same wire going to those lights. The only difference is the turning side light is affected by the turn signal flasher, causing blinking, while the other side- the non turning side-does not go through the flasher relay, but straight to the bulb from the turn signal switch. Change your turn signal switch and I believe you will solve the problem. Let me know, okay?

May be the parking filament in the bulb as the turn signal and brake lights are separate from the parking lights .

There are 2 fuses for parking lights left and right side. so it can be 2 relays. located in the box in the front.

take it to a body shop

Sounds like a short in the socket or a bad ground.
The parking light is one circuit and the brake turn signal is another.

Its not a fuse and I doubt it is a switch.
The most common problem is a bad ground going to the bulb.
If the three circuits going to the bulb are ok, it might be in the turn signal switch.

check for power and ground. One should be at battery voltage and the other ground. Somet5imes ground can't handle the current from the bulb so try to make a connection to ground. I try to either use the fuel tank or run a wire from the battery.
Second reason the turn signal switch can go bad and keep the battery voltage from reaching the bulb. I will also assume you checked the bulb on the other side that you know works fine. I use electrical contact cleaner inside turn signal switch. Move the lever
rapidly to clear any possible dirt.
Mage Talesin

I am assuming that the right (passenger side) turn signal light (blinker) is working fine. This will usually mean that the electronic flasher is not malfunctioning due to the fact that one side still works.

Since the right side brake light is working, I can also assume that the brake light switch is okay.

It is possible that more than one bulb may have been out. The quickest way to test this is to turn on the hazard lights and slowly walk around the vehicle. Make a note of which lights are flashing on one side of the car and compare that to the other side. One bad turn signal bulb (front or rear) is enough to prevent that whole side from blinking. It is also possible that a single bulb is responsible for both turn signal and stoplight. Make certain that the bulb that was replaced was not the back-up bulb. Replace all other bulbs found to be burned out.

And finally, check to see if there is power to the bulb socket. If it is a double-contact socket, there should be power to one of the contacts for "parking lights", while the other contact should be for "brake lights". Make sure the correct bulb was installed.

Check the ground on the passenger side rear lights, it's likely bad. As for the hazards, sounds like a bad flasher or fuse.