I'm a licensed mechanic in Canada and I have a 2005 Dodge Ram in my shop with this exact problem. I diagnosed it today and determined that the fault lies within the fuse box (may also be referred to as the Front Control Module [FCM] or Integrated Power Module). To be more specific, I discovered that the park light relay was missing 12V constant on pin 85. I have 12V constant on pin 30 (normal), 12V on pin 86 (normal, switches to ground when park lights demanded) and when I add 12V to pin 87 all the tail/park lights operate.
I did some searching online tonight and I have found numerous forum posts regarding this issue with many individuals having to replace the fuse box. Some individuals even commented that the fuse box was on back order due to demand. I hope this information helps.