The power jack is connected directly to the batteries and if you disconnect the battery elsewhere with the battery disconnect switch, the jack will still work.
I am guessing you used the battery disconnect switch, but I never have and many others don't either. Turn it back on and let there be light.
If you plug the trailer into shore power, the lights should work regardless. But if you charge the batteries with shore power and the single stage charger Airstreams come with, you will eventually overcharge them and dry them out. There's a lot more to learn about batteries and I suggest you look for threads on them.
There are no lame questions, though there are some dumb answers.