First there may be a main battery fuse or circuit breaker that is blown or tripped
Second many low end units of that era had Magnetek 6300 Power distribution center/converter/charger unites.. El-crapo converters but in these units the converter and the charger are differente modules. the charger is small. around 3-5 amps and dumb (it keeps on charging even if the battery is full. thus boiling the battery dry and killing it) and the converter is not much better since it outputs rectified AC which is a long long way from true DC.. But is ok for things like lights that do not care how dirty the power is.
When you unplug there is a relay that is supposed to connect the battery to the lights. It can fail
Recommendation if you have one is a progressive Dynamics 4600 series.. This replaces only the rear portion (The elctronics) of the panel. you keep the same fuses and circuit breaker part but the back part is upgraded to the best 3-stage converter made..