There are two systems in the trailer, one 120 volt system that you've noticed is working, and a second 12 volt
DC system that appears to be not working. Normally there is a converter (in that era called a "Univolt") that takes the 120 volts AC and converts it to 12 volts DC to power the 12 volt
system even if there is no battery, but it sounds like yours is either toast, missing, or unplugged/turned off. Or hooking up a charged 12 volt
battery should make the lights work.
Note the univolt, even if it is working correctly, isn't a great converter. Newer converters do three or four stage charging and are much easier on batteries; a working Univolt will overcharge batteries pretty quickly.