I traced the wires from the plug on top and the -ve (Black) goes down to the black connection box at the front of the trailer, behind the battery and ties in with the other black wires that are grounded, The +ve (Red) was connected to one of the breakers to the left of the Black connection box, which means it is connected to the battery.
I did not want to cut into the wall, so I bought a plastic electrical cabinet with a clear hinged door and mounted a solar controller
Solar Charger in that
Box. In hindsight, I did not like the controller being so visible, so I blacked out the clear door. The cabinet is mounted to the side of the A frame close to the batteries.
I did not want to throw away the new battery that came with the trailer, so I just bought a second one to match. I think the batteries are 60Ah standard, which gives you 30Ah useable, with a second I get 60Ah usable.
I added two 100W panels. As you said, most stuff in trailer is 12 volt except the TV, so I bought a 200W inverter, which works great.
Inverter
I also installed USB and 12v Outlets on each side of bed, which allows for phone charging and 12V fans to run at night.
Setup seems to work well, although I have not pushed it yet (Running heating all night and watching TV..)