South East running TC since 1970 and we have always run it on the truck and I have never been stopped or questioned. I'm based in SC, the TC is considered cargo and it's illegal to attach the plate to cargo therefore it must remain attached to the truck.
My sister is in TN and was not required to register the truck camper. While not required, I think she does move it back forth but isn't a requirement.
While I do have an 8' TC, my steps somewhat blocks the license plate, but anyone in a car directly behind me can see it. Unless of course I'm pulling the boat which doesn't have a tag on it, then it can't be seen from another vehicle.
A good test is sit in a car 200' behind you. If the tag is visible, odds are you will never be bothered as it can be seen by an officer behind you.
