Toyota Repair Problems? Ask a Mechanic for Answers ASAP
Without having some type of testing equipment it is difficult to proceed to tell you what's going on. Can you at least get a simple 12 V test light from your local parts store they generally are less than $15 for a simple clamp on style test light.
Locate the four pin electrical connector going to each taillight assembly in that four pin connector you will find a green wire with a white tracer. Make sure you have a good clean ground surface for your test light preferably the door striker where the trunk latches onto something that is clean and free of paint then carefully back probe the connector and have good contact on the green wire with a white tracer on the pin. Have someone depress the brake pedal and the third brake light comes on does the test light illuminate at either one of these pins on both sides? If it does this is not electrical supply problem to the lights it has to be an issue with the contacts inside the sockets for the bulbs or in the lens assembly itself of the sub harness. Let me know what you find with this.