Yep, the converter unit in the trailer has a small battery charge output, which is enough to run some lights on the short term. It's not recommended to do this long term, but it can be done.
Similarly, your tow vehicle is wired with a charging wire, which the trailer has direct wired to the battery to charge it.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR