Looks like your Furion connector is on the side of your trailer. It is probably directly wired to the resettable fuses close to the battery. The most simple and easy way to add solar to your TT is to add a portable suitcase type kit. We use a Zamp 200w kit for our Cougar. I'd recommend Zamp, Renogy or Go Power. Look at their web sites for portable or suitcase kits. These come with the solar panels, controller and connecting wire to attach to your Furion connector. You may need an adaptor for furion connector to the kit. The portable option eliminates the need to attach the panels to the roof (they sit on the ground) and run wiring to the batteries. This will give you a reliable, easy and efficient battery charger to keep your batteries topped off when camping without hook ups.
Those of us who regularly dry camp or boon-dock use at least two batteries, either 12vdc or 6vdc. The solar kit acts as a trickle charger to recharge the batteries during the day so you'll have power for lights, water pump and furnace etc during the evening. The batteries store the power from the solar kit. The solar kit recharges the batteries.
All of your 12 volt accessories run off your batteries. I'm a disciple of the "KISS" principal. Easier is always better
Not being tied down to full hook up RV sites open a whole world of camping options. Making your TT self sustaining allows that to happen.
Hope this helps. Happy Camping!!