Based on your description, it does sound like the clock spring may have failed. I looked through the schematics for the horn and CC and both use the clock spring.
As far as the 3rd brake light, it receives power directly from the body control module. Since it works with the key off, I'm questioning if there is a ground issue causing the ground path to be interrupted when the engine is on.
Try this. Pull the 3rd brake light out from the body. There will be a violet wire with a white tracer that supplies power to it. Using a test lamp and a known good ground, see if there is power to the light when the engine is on. If there is, check the black wire for continuity to ground with the engine off and again on.
Here is a link you may find helpful:
https://www.2carpros.com/articles/how-to-check-wiring
As far as the clock spring, I attached the directions for replacing it. See the pics below.
I hope this helps. Let me know if you have other questions.
Take care,
Joe
See pics below.
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Friday, September 24th, 2021 AT 7:32 PM