When I got my 1300 there was nothing in it at all for 12v wiring or loads.
There was a shore power cable that merely powered a few 120vac lights in the trailer.
I installed a battery and quality charger and the connected a distribution panel directly to the battery and then light
to the panel.
This allowed the lights to run off of the battery whether the charger was plugged in or not.
If the charger was plugged in the the battery still supplied power for the lights and it was also kept charged.
Nice and simple.
The converter you have is probably just a 12vdc transformer and that is it.
Without any provision for battery charging anyway I don't really see the utility in keeping things connected to the converter for you now.
This way all loads run off 12vdc whether 120vac is connected to the charger or not.
For loads under 10 amps total I was always fine and had plenty of power and no worries.
Things were easy then and I could move the trailer by hand.
What year Trill is is?