Hi:
I just went through the wiring schematic for this vehicle. Power is supplied from the switch to both rear lights and the center high mount brake light. With that, if one works the others should. The only areas that I see may cause is an issue is the ground. Both rear brake lights have a common ground and the third brake light on the cab has a different one.
With that, there is a chance once you start driving, power is lost. Take a look at the attached picture and see if you can locate the ground and check it. When you look at the picture, it appears that they are two separate grounds, but they have the same number indicating the same ground. If the grounds are good, I suspect you have a partially broken power supply between the switch and the lights causing an intermittent issue. We will cross that bridge if needed.
Also, I want you to try something. If the ground is good, turn the hazard lights on and drive to see if they stop working.
Here are a few links you may find helpful:
https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester
https://www.2carpros.com/articles/how-to-use-a-voltmeter
https://www.2carpros.com/articles/how-to-check-wiring
Let me know what you find.
Joe
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Wednesday, November 6th, 2019 AT 7:22 PM