At night when my headlights are on the back tail lights won't light up. The brake lights work as do the 4 way flashing hazard lights. If it is a fuse blown, I assume it would be under the steering

Check for Power on your License Plate Light, more than likely you have lost GROUND

Turn Signals, Do the Front Work and the Back don't? If NONE then FLASHER FUSE

Check your fuses. I had the same problem with a 90 Honda civic. Dash lights went out, tail lights also went out. Replaced 1 fuse and all came back on.

Could be the headlight switch.
The switch has two sets of contacts for the parking lights, the park position and headlight position.
You may need to check the circuit at the switch to see if you are loosing power when the switch is moved from park to head.

Wow !! Where to start ??

I think most if not all of the lights go thru the ignition switch. What I mean is the ignition switch must be on for the lights to work.
Most of the lights are on different circuits with different fuses and relays. They are connected to the battery and alternator but not directly. Most but not all are connected to the headlight switch.
One thing that does tie everything together is the grounding of the car. All voltage goes back to the battery by way of the steel frame of the car.
If a ground strap or cable is loose or dirty, electricity has problems getting back to the battery.
So the options are the headlight switch, the ignition switch, and the ground circuits.
I would start by checking the tail lights or headlights to see if they are getting 12 volts, then check and see if the lights are grounded back to the battery. I've even run a wire from front to rear to bypass the car ground connections to test.

I think you have a bad ground at the back on both rear lights or their earth out on the same connection but these american cars use a funny system where the stop lights are the indicators and not a seperate yellow light like europeon motors ,Now these brake light switches also allow the indicators to work by shutting off the feed to the stop light so it flashes with indicators ,Why american cars use this system i dont know as its so complicated for the stop light switch function but try the ground or earth wire on the back lights and if no joy then ask a american mechanic with experiance of this sort of circuitry as when i get american cars for import i have to fit new back lights and disconnect the brake light switch .

I had this problem with my 2007 Honda CRV -- all the lights worked EXCEPT the tail/running lights and the license plate light. The other tail lights worked -- brake, reverse, indicators, and hazards. Front headlights also worked, but when the headlights went on the back tail lights did not (not to safe for driving at night!!)
The fuse was #15 in the interior fuse box (under the dash driver side) with the label "small exterior lights" ( also check fuse #19 labeled "small lights main"). The cause of my problem, I believe, is a bad or lose wire in my license plate light.

I hope I'm wrong, but sounds like a wiring harness malfunction possibility. Back in the late 70's, I had a '67 VW van. At night, when I'd turn off the ignition the engine would turn off, as it should IF I TURNED OFF THE LIGHTS, BUT IF i TURNED THE LIGHTS BACK ON AS THE ENGINE WAS SHUTTING DOWN, THE ENGINE WOULD RESUME RUNNING.

Tail lights, parking lights and dash lights are all on the same circuit...I'd go to the fuse panel under the dash and check the fuse for those lights....usually referred to as accessory lighting in the owners manual and is usually a 10A fuse.

Hope this helps...

There is a circuit breaker inside the headlight switch body. It gets weak over time and use. The breaker is actually mentioned in the owners manual. A new switch is about $75.00 at the local parts store. You must remove the front of the dash to change the switch. Mine would go off and then in about 30 seconds reset and the lights would come back on. I would be driving down the road with my headlights flashing as the circuit breaker opened and closed. New switch = problem fixed.

From what you are describing it sounds as if the headlight switch has gone bad.  That switch controls not only the headlights but the tail lights and all dash lights.  Everything that IS working is connected to other switches not related to the headlight switch.  You can either buy a new one or get a used one from a junk yard or ebay.  Pay particular attention when getting a replacement as there are 3 different models which vary depending on options such as Auto mode and Foglights.   Replacement is easy.  Using a flat screwdriver carefully pry off the trim cover around the switch. The switch is held in with some screws.  Be careful disconnecting the wires so as not to break the locking tabs. The trim just pushes firmly back into place.