How my insurance guy explained it to me (Country Insurance) is that the TT is indeed covered while it's physically attached to the truck under the trucks policy..
Once the trailer becomes unhooked for whatever reason, it's on it's own and would need it's own coverage.
It's interesting what's been said about home owners ins covering it while camped, but in my case, the ins guy said my home policy only covers it when it's physically on the homes property.
His examples were like this..
Scenario 1. Traveling down the road towing the trailer, I turn too sharp and hit a parked car with the trailer. Truck ins covers this.
Scenario 2. Traveling down the road towing the trailer, the trailer becomes unhitched from the truck and before it stops, it hits a car. Trailers liability ins would cover this. (if no liability ins on trailer, I'm stuck with the bill... Truck ins would not cover this)
Scenario 3. Trailer parked at home. Tree falls on it. Home policy covers.
Scenario 4. Trailer parked at home. Somehow it rolls off of my property into the street and hits a car. Trailer liab ins covers.
Scenario 5. Trailer parked at camp site. Somehow it rolls away and hits a car. Trailer liab ins covers.
I'm sure there are a couple more, but I'm just saying that's how it was explained to me by MY ins guy...
Your state/insurance guy might be different, so you'll need to find out what specifically works on your end.
My additional liab ins on the trailer only added around $30/yr.. I think I only pay around $150/yr to full coverage on my TT.
Mitch