I have the exact same problem. 3rd light works when pedal pressed. Lights work fine when lights turned on. Brake switch appears to work fine at least for 3 rd light.
I replaced the bulbs. Fuses must be ok because third light works and the bulbs work

 

Well your first step should be to check the wires with a test light like the OP did and see if that's where your problem is

 

Hi,
could the wires be bad at the bulb if the bulb works when i turn on the lights?
I looked for the connection where the 3rd brake light comes off the wiring trunk and it is all encased in plastic shroud. Should i open the shroud and look for the connection he described.

 

There's separate wires for the brakes & for the taillights. One wire could be corroded or loose, worse than the other wire.

 

I have exactly the same problem, rear brake lights do not work, only the high mount brake light works.

I tested the voltage between 1 (Source) and GND, 2 (safety indicator) and GND, 3 (brake light input) and GND, and 6 (ignition input) and GND, only safety indicator show some voltage and the rest of them do not. Anyone know what could be the root cause?

 

The problem for me, was a little box at the bottom of the driver-side tail light. Take your time getting there...
Remove the module under the driver-side rear brake assembly. It was difficult to disconnect, a flathead screwdriver addressed that problem. I was finally able to disconnect the connector from the module, sprayed both connectors with WD40 to clean the contacts, and the problem was corrected.

 

Exactly what year do you have, trim level (EX, DX, Coupe, sedan) would also be a plus. I have a guess based upon your question but knowing would be better...........VERY good idea is to add your car info to your signature, be sure to display your signature, that way you don't forget

 

what do you do if the sensor is bad

 

If you are sure the sensor is bad, then you will have to replace it or repair it.

If you tried cleaning the contacts in the electrical connector and box with contact cleaner, then you probably need to replace it. It looks like a simple circuit board, so you may want to look at the solder joints to see if the solder joint cracked over time. You can try reflowing the solder joints on the board.

I remember reading that unbalanced loads on the bulbs can trigger the brake lamp light. You can try replacing all the bulbs in the back of the vehicle to see if that fixes the issue.

 

Exactly what type of car? Why do you think the senor is bad?