The tail right light goes off, while the left one is red. What could it be?

Have u tried to unplug the light and re plug it in or checked the fuse box inside the car?

are you saying that the rear marker lights are on and then you step on the brake and one side side marker goes off while the other side brake light comes on? if that's what you mean then i would check the bulbs and sockets first ,fuse should be ok since the power is there.