I'm dealing with a similar issue.
My Driver's running lights are out, but the brake, turn, and headlight work fine.
You might have similar issues but a different pattern of just rear running lights.
In my troubleshooting, I've checked fuses, and nothing was blown.
I even replaced my TIPM with a new one, and it didn't resolve it.
I was still tracking it down when I came across your post.
I hope I can figure things out and shed light on it.
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