Yes, it is a mess. Here is a suggestion for how to proceed. It is what I would do at any rate.
1. Get a charged 12 volt
battery and connect the - pole to the frame. Most likely you can also connect it to the large white wire which is usually the negative one on all Airstreams.
2. Connect a 15 amp fuse and test wire to the + pole of the battery. Have extra fuses available.
3. Find the original trailer battery location and tape the ends that went to the battery. Do not plug the trailer into 120 volt power, in case the Univolt is still operational.
4. Touch the end of the fused wire to each of the smaller wires that are available, except the white ones. If the fuse does not blow, walk around and look at the lights, you may be lucky and find the marker lights, or tail lights, or right or left brake/directional lights operating. Mark each wire as you identify what it connects to. However, be aware that even if you find a wire which does nothing, it may be connected to a rusted socket or missing bulb in the rear lights, and needs to be repaired on that end too.
If you hear a click, you may have identified the brake wires. A compass put near the brake has also been used to identify when the brakes are activated, but I have never used that technique. What you are looking for, in this step, is which color wire goes to which item, directional lights, marker lights, and brakes.
The brakes are usually a larger wire than the others, and may be yellow on your year of AS. As I recall the charge line to the battery is often blue, but don't rely on any of that with the mess you have. The brake wires may be a pair, in a sheath like household Romex wires but more flexible. If you find anything that looks like that one side connects to the white wire (negative) and the other to the brake line from the Tow Vehicle. Both have to be connected to make the brakes work. It is also common that the lines to the actual brake magnets are corroded off, near the brake drum and each will need to be inspected and repaired.
The other large wire, blue, or black commonly, may be the one which goes to the trailer battery as a charge line, and also to supply the break away switch and power jack up front.
5. Once you identify which wire is for which system (brakes, charge line, right turn, left turn, marker and possibly back up lights) you can buy a pre made up umbilical cord with the now common Bargman type flat blade connector on it. It should come with a wiring color code telling you which colors are for each function. Then connect it up to the wires you have identified in the steps above and presto, changeo, you may be in business.
6. You can also send me a plane ticket and hotel reservations, and I might do it for you....lol. Also, a nutcase like me might be available locally at the WBCCI meetings who could help you out.
I hope this helps.