Tail lights not working

Somewhere in the wiring you have a bare wire that is touching to ground, which on an old truck is kinda common, there is nmot quick fix or one thing that is causing this, you need to check the whole wiring harness from the switch to the taillights. Here is alink to a poss source of wiring diagras for the truck. http://bbbind.com/free_tsb.html

Tail light problem '1986 Dodge Aries 4 Door - faqqq

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Question Product: 1986 Dodge Aries 4 Door Question Details: Tail light problem I ...Most people suspect a bad bulb and when they go to change it, it lights up.

They are separate bulbs.
are you saying you check both of those bulbs?
if you did, and the taillight/marker light is a good bulb, then it's either the bulb receptacle, or the wiring going to it.

If you are not getting power from the headlight switch for that circuit, but the other side works, you'll have to trace the wiring. The socket has two wires plus a ground. One wire is for the tail lamp circuit and the other is for brake-turn signal.

There are a total of six fuses that control exterior lights and dash lights. Check all of these Fuses: 10, 21, 3, 7, 13, 33
Does the high mount stop light work when you apply the brakes?

Check your fuse marked Taillight in your fuse box......This should get them back on..

Even though the relay is activated,I assumed you checked the out put?Also,You checked the voltage at the light sockets?With a meter,or test light ,check the fuse for the cluster lps,adjust them to dim,and to bright,the meter should act accordingly on the fuse.If it does not,replace the dimmer control,or head light switch,witch ever controls them.This may allow continuity to the tail lights as well.If the fuse is dead for the cluster lights,replacing the dimmer control,or head light switch will solve the problem,or,from another fuse ,supply voltage to the cluster lp fuse,one that is only hot with the key on,cause if you do this the dash lights will come on,every time you run the vehicle,day,or night.

from a haynes or chiltons repair manual,but check under the rear of the box by the bumper for corroded wires from the main whip where each taillight whip connects together.un-tape the wire covering and look at each wire and test for power at each wire.Brown wire is taillight,black is ground,and i think yellow is for brake on 1 side and green for the other side

check connections and fuse for taillights