Dutch one option you can consider if you want yo use the selection box is to buy an av-to-coax converter. They are cheap, probably under 10 dollars. That would allow you to go from the video/audio plugs in the 211z to the satellite in on the selector box, then use the existing cable connector at your TV.
You would lose hd picture doing it this way.
If the park cable inlet does work I would personally bypass the selector box, keep your 211z by the TV connected by hdmi. So you would connect tailgater to park cable. Where cable connects to selector box bypass that and try and connect straight to TV room with a simple cable-to-cable connection. Then plug the 211z into your cable jack by TV. Hdmi from 211z to TV.
Unfortunately you might have to start as direct as possible, test, then try adding another step and see if you can get a signal.
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2013 F150 FX4 EB