Dick Feller - a.k.a. Deena Kaye Rose, wrote this song with Sheb Wooley for the "Kickin' Asphalt" compilation. Again, Discogs says this song features Feller, but no other sources do. There's no question it was written by both, so it's now credited that way.

There's even a question about the title. It's possible the full title is "Come On Back To Nashville & Get Your Peterbilt" - presumably because there's already a Tom T. Hall song with the shorter title.