I don't know about Tennessee, but the most logical insurance for a trailer RV is to simply add a rider on the current automobile policy. And then, it depends upon how much insurance and what you want insured too.
When actually towing, the trailer is usually covered under the auto insurance policy. NOT full coverage, but property damage and liability ... for example if you back the trailer into another vehicle.
If you want full coverage, replacement coverage, coverage for theft, fire, vandalism, natural disasters, flooding, paint, or electronics, when the trailer is NOT connected to the tow vehicle (and actually for when it is too) ... then a separate rider on the auto policy is needed.
There is one more "insurance" you need to consider ... "slip and fall" type insurance. Say you are parked at a campground and someone trips over your water hose. This is not the campground's fault, it's your fault because you laid out the garden hose and it was determined you were negligent. You get sued for negligence (not the campground). You loose. Insurance pays the "damages". This is usually covered under "homeowners" insurance (at least it is for us).
Our "homeowners" insurance also covers any "theft." The way our insurance agent explained it to us.... if you took the trailer and turned it upside down and shook it.... everything not attached that falls out is covered. Computers, televisions, weapons, dishes, clothing, pillows, toothbrushes .... everything. A cost would be determined for the "loss" on these items separate, and that falls under "homeowners" insurance.
So, adding a rider on the automobile policy is usually not very costly at all, as basically the insurance covers theft of the trailer or a natural disaster event or fire or vandalism.
So, these are all the options one needs to consider. If the camper still has a loan against it, loan companies will require full coverage so if the trailer goes up in smoke, they get their money back regardless. This is always a separate policy or rider on existing auto policies.
If there is no loan on the trailer, then the standard automobile policy will carry the property damage and liability and usually at no additional charge. Just like for an automobile, this is the bare minimum required by law. Any other insurance is gravy insurance. Not necessary, but you take the loss if you don't have the insurance.