The Furrion "sound bar" is really a "reshaped RV stereo system without the DVD player"... They just took the "base model electronics, deleted the DVD player and made it long and skinny like a sound bar and started selling them to RV manufacturers for $50 cheaper than the ones with a DVD player and a square shape.... Guess what..... Yep, every RV manufacturer is now installing "sound bars to augment your TV".. but they aren't really sound bars, just cheap RV stereos shaped like a sound bar....
All that said, don't expect much more than a radio with poor reception from your Furrion sound bar.....
As for television sound, you might try an audio headphone jack from the TV headphone jack to the "sound bar aux input".... That "might get you sound" but it won't be "HDMI or Optical Cable quality"..... Of course, with the air conditioner running along with the range hood vent fan, who can hear the "quality sound" anyway.....
It's a "good thing" that we buy these trailers to "commune with nature" not to "enjoy audiophile quality entertainment"..... YMMV
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS