My rear driver-side turn signal and brake light aren't working (the reverse light does function). It started out as an intermittent problem, then it stopped completely. I replaced the bulbs, but that didn't help.Is it just a wiring problem? Can I do it myself?

take it to a body shop

Check for loose contacts or wiring that is causing a short circuit near the brake pedal, or at the rear light.

You will need the facxtory wiring diagrams you can buy the booklet here.

Bad bulb ,& or socket

{: ) Looks like your lightings got haywired. Have you had vehicle repairs recently? Anyway, it seems that you have poor grounding connections for the affected lightings. Some circuits share common ground, and ground terminals are strategically distributed on the vehicle. If these grounds don't have good contact with the body, chassis, or engine ground, circuit functions are badly affected. Thats why these ground points should be inspected and kept clean and tight, maintain that good wire and terminal contacts.
We can start with G100 located at the Left Front of the Engine Compartment on the left front body mount. See diagram below:


Check out also G401 which is located in the chassis harness, mounted to the left rear Body mount. This ground point is shared by the rear lamps like the brakes, reverse, and rear signal lamps.
If possible check also other ground points that you may visually come across while on your search. Be sure also that fuses are all inspected good.
I hope we get lucky in finding and fixing a certain lamp function, if not all. Goodluck.

You have a bad connection at the rear passenger side turn signal. It is either the connection is corroded or a wire is loose on the ground side of the circuit.

If you are sure it is not corrosion at the bulb sockets then it could be the back-up switch at the transmission.

Bad earth connection.Clean or replce wire.

Hi
You may just have a bad earth in wiring on the lighting or your light control modual could be fuilty has any one tested this for you
Paul

This is a classic example of turn signal switch failure. On GM vehicles with a multi-function turn signal switch and combination stop/turn/tail lights (all rear lights are behind red colored lenses except for back-up lights) The brake light power is routed through the turn signal switch. This makes it possible for the right rear light to function as a stop light while the left rear turn signal flashes, and vice-versa. When the contacts fail to remain constant the brake lights, and turn signals can become intermittent. The proof that the brake light switch is functioning correctly is that the high center (cyclops) brake light functions properly. Wiring integrity is verified if you can prove that turn signals operate, but that can still be intermittent with this complaint, BUT if you use your hazard switch to turn on all the signals at once, you can verify wiring integrity. This is because the turn signal, and the brake light use the same circuit, and bulb filament in the rear lighting assembly. If any Hazard lights fail to function, check bulbs first, then retest. If all Hazrd light flash correctly and reliably, bulbs, sockets, and wiring have proven integrity, and the turn signal switch is the remaining component in the system which needs to be tested. Unfortunately, this switch requires disassembly of the steering column for service, testing or replacement. If you have never disassembled, and successfully reassembled a GM tilt steering column, I would reccommend professional assistance.