97 Olds Aurora, headlights go on, tail and dash goes off

You have a bad ground. The frame of your Jeep, (As in most vehicles), is the main ground source.
All ground connections go to it, via some sheet metal, or directly. The ground wire from your battery will be connected to your frame.

Your headlights will pull at least 30 Amps. So will your taillights when the brake, and main lights are on.
Since you have a bad ground, (Or Grounds), your ground source cannot support both headlights, and taillights. Your dash lights? They should be on the same circuit as your taillights.

How to solve this problem?

1.Start with the the two ground straps, that are supposed to be connected somewhere on the back of your engine, and lead up to the firewall. If you have had any mechanical repair, and it involved removing the engine, or a cylinder head, (Or two if you have a V6), the mechanic may have failed to connect Both flat ground straps back up. Or one, or more, of the ground straps are loose, and/or corroded at the connection to firewall/engine.

2.Checked okay? Go to the front wiring harness. Out of this harness will be wires going to the headlamps, and turn signals. There will also be one, or two wires that are a ground. They should have a round metal terminal end on them. They will connect to the front sheet metal somewhere.
They may be loose, and/or, have corrosion under the metal terminal to the sheet metal connection.
Remove the terminal end, and check for corrosion. Use sandpaper, or steel wool to clean the contact surface of the sheet metal, and the terminal end. Lightly coat the terminal end with a corrosion inhibitor you can buy from your local auto parts store. It's in a spray can.
No problem so far?

Check each headlamp socket for corrosion. Means removing the headlamps. (Yes I know. Pain!)
If your Jeep uses Krypton bulbs, don't touch the bulb with your fingers. Use rubber gloves, or a Very clean rag. The oil off of your fingers will greatly diminish the life of the bulb!
Okay so far?

Go to the rear of the vehicle. Check the rear lighting harness, and it's ground connections. Check the lamp sockets.

This is typical of a gremlin in the grounding of . . . something. These are no fun to chase but check for common grounding points under the hood. That the dash lights go out when the headlights are turned on means that the lights are causing the voltage that should be available to other areas is being dropped across the bad ground.