Man oh man, these types of issues are ugly, and an owners worst nightmare.

If it would just fail solid, finding a comfortable fix is so much easier.

Most of my ideas were covered, as I would probably goto a ground run, RCM, or somewhere in the Battery or cabling.

You said it happens at idle, just curious if you ever experienced it at speed when driving...???

Now that would be coyote ugly in my mind...and very dangerious...