My 1992 GMC Serria has an electrical problem. I have no taillights, no brake lights, no hazard lights,etc. I traced the wiring to a connection on the firewall, which is located below the cruise control module. This box has three connections going to it, one to the headlights( they work fine), one to the taillights, one to (not sure). I would like to know what this box is called, so I can order a new one ... Connection going to taillights looks burn't or melted. Your advice is greatly appreciated

First check all your fuses.
https://www.google.com/search?q=cig+lighter+fuse+panel+on+92+gmc+half+ton&biw=1361&bih=650&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwj_--aUpbvQAhUE4yYKHTvTBg4QsAQIKw#tbm=isch&q=1992+GMC+C1500+fuse+panel+location

If all fuses are good, you may have a wiring problem. If you are mechanically inclined, will need to remove the required components to expose wiring and see if you have a break somewhere. Most wiring harnesses run along inside of vehicle trunk. Then, they continue under rear seats and possibly under carpeting.

Make sure all bulbs are working. All blinkers, tail lights, brake lights etc. I know you mentioned most of these lights work, however it only takes one light to throw off several others. Trace wiring from each as far as possible to locate a possible break in the wiring (shorts). Also, check the headlights and make sure they are plugged in all the way (even tho they work). Also check all relays. One dirty connection can cause all sorts of problems. Jeeps also are known for their poor wiring and common electrical issues.

loose connection ? check all wires from battery, clean battery & terminals, check alternator wires, grounds, etc., thoroughly check all grounds, everywhere !!!!!!!! inspect the headlight switch for loose connection, trace all power wires & ground wires for loose or bad connection . what else could it be ?????????????/ check all wires, especially back to fuel pump, rear tail lights, etc., make sure those ground wires are making a good connection, DO YOU UNDERSTAND ??????? I CAN'T EXPRESS THIS ENOUGH !!!!!!

your turn signal switch could be bad

Try wiggling the hazard light switch while pressing on the brakes.The taillights are connected to the turn signal switch before it goes to the brake switch.The contacts on the hazard switch are probably dirty(I remember this problem years ago,same symptoms-3rd light works but l/R tailights not working).You may just be able to turn the hazards on+off a bunch of times to clean the contacts instead of replacing the switch.

if your fuse is good. and you have power at the brake light switch and when you hit the brakes you have power coming out the otherside of brake light switch/which would be the white wire/ check that the white wire is sending power up the turn signal switch. if theres power there and your turnsignals work? im afraid that your turnsignal switch is bad rare but it has been known to happen.

Sounds like a bad earth/ground. Check your earth connections.

Maker sure your flasher is ok and that you are getting power you will have to trace it from there

The tailight markers and plate lights are wired together. A fuse to the marker lights or sometimes called,park lights, may be blown. You may have a naked hot wire rubbing metal. Sometimes SUV's have trouble with trailer light plus also that ground out the circuit.

it seems you have a short in either one of the lights or interlock. all are connected to the same fuse. trace the wiring from the fuse box back to the component. Using a test light test in between the wires. check for any obvious breaks in the wiring.