Yes the multifunction switch contains the turn signal lever,hazard switch,etc, The circiuts for the brake lights run through it. The third brake works because it runs a different path, so you always have at least that brake lamp. If you wanna check a little deeper, i believe a yellow wire coming out of the switch goes to left side and a green wire goes to right side, we know you have power going in on the white wire, If you do have power on those wires, then your problem may be in the back of the car or a wiring harness problem somewhere. If it turns out to be the multifunction switch, here is the removal procedure. You can get by without taking off the wheel if you can get a small wrench on the front bolt, with covers removed. Remember all plugs have to be connected to check the yellow and green wire.
Multifunction, Turn Signal, and Hazard Switch Replacement - On Vehicle Removal Procedure
Caution: Unless directed otherwise, the ignition and start switch must be in the OFF or LOCK position, and all electrical loads must be OFF before servicing any electrical component. Disconnect the negative battery cable to prevent an electrical spark should a tool or equipment come in contact with an exposed electrical terminal. Failure to follow these precautions may result in personal injury and/or damage to the vehicle or its components.
Notice: Use the correct fastener in the correct location. Replacement fasteners must be the correct part number for that application. Fasteners requiring replacement or fasteners requiring the use of thread locking compound or sealant are identified in the service procedure. Do not use paints, lubricants, or corrosion inhibitors on fasteners or fastener joint surfaces unless specified. These coatings affect fastener torque and joint clamping force and may damage the fastener. Use the correct tightening sequence and specifications when installing fasteners in order to avoid damage to parts and systems.
Tighten Tighten the screws to 6 N·m (53 lb in).
Let me know if you need further assistance. Thanks Eric