While there isn't a single definitive instrumental track titled that dominates the charts, the name is frequently used by bands like Rusty Nail (an Irish rock band from St. Louis) or associated with instrumental versions of songs like Moderat's "Rusty Nails" .
To live up to the name "Rusty Nail," the music should reflect the qualities of the object: metallic, aged, sharp, and perhaps a bit dangerous. Rusty Nail - Instrumental
Ensure the song has a clear beginning, middle, and end. You can start "clean" and gradually add distortion (the "rust") as the track progresses. While there isn't a single definitive instrumental track
Use "biting" guitar tones or distorted synth leads to mimic the "metal" aspect. Rusty Nail - Instrumental
Use tools like LANDR or PhonicMind to isolate the backing tracks from the vocals.