Sounds like the TV should be plugged into a duplex that is fed (powered) by an inverter, but I know nothing about your coach model. Time to get on the phone with Entegra and learn about your inverter and your electrical system.
There are going to be very few similar owners of identical coaches on this forum so a fast call to Entegra is gonna get you answers faster than waiting for one on this forum, I believe. Could be wrong.
And yes, coach manufacturers don't want drivers to be watching TV while driving, so may just need to be plugged in elsewhere.
Gary and Dee, Zowie and Bowie (traveling cat sibs)
2019 Cornerstone 45B, X15-605hp, Imperial, Spartan K3,
2013 Honda CR-V toad, Demco Excali-Bar II,
Demco Baseplate, Demco Toad Light system, 73 de W5FI