Do you have any solar panels installed on your trailer? If so, that solar port should indeed be wired directly into the input side of your solar controller, in parallel with the pre-installed panels. Otherwise, I believe you just have the solar prewire option, and I don't think that port will be connected to anything.
If you do have solar, and as long as the trailer is not stored under full cover, the rooftop panels will be more than sufficient to keep the batteries charged while the trailer is stored. No trickle charger or shore power connection required. If the trailer is covered, you could connect a small auxiliary panel (with the same open voltage rating as the rooftop panels) to that port as described above. If you have solar but still prefer to use a trickle charger, it would have to be connected directly to the battery.
I'd also recommend disconnecting the main battery switch found under the dinette bench while the trailer is in storage/unplugged from shore power. This will disconnect the battery from the converter and all the 12v systems, but the solar controller will remain connected.