Defective stop light switch or fuse.
Have you replaced any tail light or turn signal bulbs lately? It is a common mistake to replace a combinaton turn signal/tail light bulb with the wrong one. I ran into this problem on an older buick. I replaced a bad turn/tail bulb with the wrong bulb. The new bulb fit but when I stepped on the brakes the dash lights would come on. What I did wrong was I put an 1156 (single contactor bulb) in the turn tail socket which was supose to take an 1157 ( double contactor bulb). Check your turn tail bulbs and make sure they are correct.
the bulb with two elements in it is the turn signal and brake light bulb
There are 2 filaments in the tail light bulb. One filament lights for the tail light and stays on as long as you have the tail lights on. The other filament only works when either the turn signal is on, or the flashers, or the brakes are applied. Have some one get in the truck and apply the brakes and see if the right rear brake light comes on. If it doesn't, then the filament is broken inside the bulb and you will need to go get a new bulb. Most pickup you just remove a few screws and gently put the plastic lens off and then either twist to remove the bulb or just pull straight out depending on the base of the bulb from the housing. Once you get the old bulb out hold it up to the light and nomally you will see one filament is still connected and the other filament will be broken. You can always go get the bulb first and see what the base looks like to determine if it's a twist and pull or just a pull style bulb.
No this isn't the reason why your tail lights don't work. Tail-lights and the turn signal are two different systems in the car: if your turn signal is broken that doesn't necessarily mean that your tail-light will be broken.
See sources and related links below for 1993 Dodge Shadow tail light, brake light and turn signal light bulb part numbers.
Fuse
Check the bulb. If it didn't help check wires around the tail light. Also you might want to check the fuse box for failed fuses.
may have the wrong type bulb check to make sure bulb has two contact points.
tail/stop/turn signal bulb # 3057 park/turn signal bulb # 3157NA
Have you checked your bulbs ? The tail light / brake light bulb has 2 wires inside it In my case I have had to change each bulb because the brake light portion did not work but the tail light portion of the bulb did ( I'm assuming that your front park lights are working )
check the bulb, it has two filaments, one for tail light, another for brake light and indicator. if the turn signal works, it's not the bulb, but a power supply problem.
1995 Chevrolet Silverado - See sources and related links below for complete automotive bulb list.