We did similar years ago when we found some 26 inch native 12 volt panels.
We made 12 volt ats units for the tv that worked well.
Needed is just a standard automotive universal relay that is SPDT.
We also found some pre made cords with matching coaxial power connectors that match the original.
Wire the coil of the relay to the female plug as well as the NO pin on the relay.
Male plug goes to the Common pin.
A fused wire to battery connects to the NC pin on the relay.
Factory adaptor PLUGS INTO ats then vehicle battery also attached.
Confirm 12 volt battery power at male then plug adaptor into power then relay clicks and adaptor power now at male connector and same polarity.
If pass plug into tv.
This allows use on ac power whenever present and on battery when dry camping.
Add power switch between relay and male plug to turn off power to tv as it always has some load so dry camping you will want to disable completely without needing to unplug.
All is plug in with no wire cutting so warranty is fine...
Tony & Lori
1989 Country Coach Savannah SE