If you need the open bed more often then covered get a roll back bed cover.
If you need your TV primarily for towing and storage out of the weather get a cap.
Spoiler Alert : What I did
Sorry not a Hi Jack.
We've been towing our Casita's since '98 with my '73 Dodge van. In 2001 we replaced it with a '98 Tahoe 2 door that I installed a bed slide in making it essentially PU with a Cap.
So when we towed our '69 25' Airstream the Tahoe just didn't feel right so I replaced it with a '14 Tundra Double Cab. I added an ARE Hi Cap for 3 reasons 1.Covered bed, 2. rear door height 3. Aerodynamics for the Airstream.
About the Cap I added a tilt down front window with slider, makes cleaning the glass possible. Added Windoors on both sides , gives great access to stuff, added headliner and 2 strips of LED Lights to the ceiling.
I also added a BedRug.
I needed an open bed so I built a pickup trailer back in '77 out of a '69 Datsun PU. In '84 I changed out the stock Datsun bed for a 8' Ford bed. A few years ago I junked the Ford bed, and rebuilt the chassis and powder coated it and added a '98 Chevy bed. Oh and I got a soft cover for the bed also.
That's my story and I'm stickin' to it