Another test is to run a coax from the rear TV coax (at the TV) using a barrel connector to the front TV. Then you know if it's the coax or TV. If it's the coax try the outside TV coax. Also remove the splitter for the rear TV.
Batwing checking is secondary to the non working rear TV as you have a good signal to the front TV.
Disconnect the 12V power to the box with a distant station to determine if the batwing is working as expected. If a wingman is not installed add it first checking that you have the additional clearance on the roof.
BTW You'll want a spare coax for the cable connection if you don't have one. Barrel connectors are available at various stores.
