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.