Hi and welcome to the vintage Airstream hobby. There is a lot to learn about your trailer and these Forums will be very useful to you.
Okay, when something electrical doesn't work in your trailer, you gotta be a good doctor and run some test to diagnose the illness.
1. Do none of the
12 volt lights work? Or do some work?
2. Do the roof vent fans work?
3. Does the water pump work?
4. Go buy a "digital multimeter" at your hardware store. Set it on DC voltage. Set it on 20 volts. Touch the black probe to the negative post of your battery. Touch the red probe to the positive post of your battery. We want to see at least 10 volts there. If less, you might have a dead battery.
5. You mentioned your "plugs" work. Some call them outlets. So you plug your trailer into 120 volts and your outlets work. Maybe your air conditioner does too (caution, don't run the AC unless you are plugged into 30 amp service. You can run the AC fan on low only, but no Low cool or High cool settings.)
6. So with your trailer plugged into 120v service, go test the battery again as in #4 above. Your converter ought to be delivering maybe 14 volts DC to the battery. If not, then your converter may not be plugged in, may have blown a fuse, or may be defective.
7. Many converters are "plugged in" to an outlet. Find your converter and confirm it is plugged in. Take a little lamp, or hair dryer, or your new multimeter and verify there is 120 volts being delivered to the outlet your converter is plugged into. If yes, then we will study the converter. If no, then we will verify there are no tripped breakers in the power distribution panel maybe located in a closet somewhere. You have to have 120v AC power to the converter. '
8. You have to figure out if the converter is delivering good voltage to the battery to keep it charged up, and if so, the converter is delivering good voltage to the rest of the trailer.
9. The converter will have a couple of fuses somewhere on it. If no lights yet, pull the fuses and make sure they are not blown, open, and kaput.
With some testing, you will likely find out the reason you have no
12v lights in the trailer. Note: All vintage Airstream hobbyists have a multimeter to diagnose problems. It is an important tool for your tool box.
David