"I don't know how I could tell whether the brake light and turn signal light are the same by looking at them with a helper, since the brake light won't come on"
Actually, I was thinking the same thing just as I clicked "Submit Answer", but by then it was too late. One thing you can look at is the idiot engineers use yellow turn signal lights on the rear of some cars to confuse the rest of us. Brake lights are always red, so if you have yellow rear signal lights, they use separate bulbs for the brake and signal functions.
The next thing is to at the bulbs through the lenses. Most of the bulbs are going to have two filaments. One is always brighter and is for the signal or brake light. The dimmer one is for the tail light. When you have, ... Wait a minute. I had a better idea. I just popped up a wiring diagram and found that your vehicle does indeed have separate bulbs for the two functions. That means the turn signal switch has nothing to do with the brake lights.
Since the center-high mount brake light works, there isn't much left in the circuit to cause problems. The two brake lights have separate ground wires, so if one is broken, the other bulb would still work.
The place to start is to remove one of the brake light bulbs from the socket, then use a test light or voltmeter to test for voltage while a helper pushes the brake pedal. If voltage is found, the next step is to test the ground wire for continuity. You might also return to the shop where the bulb was replaced and ask them to recheck their work.
Monday, June 29th, 2015 AT 4:47 PM