I had a similar problem, you might want to try changing out the BWD - Relay - Multi-Use Part #R4823. It is located under the Dash, beside the Steering Column. I purchased one from Canadian Tire for $25.00 
First check the bulb filaments are ok , some bulbs have a dual filament 5 w for tail lights 25 w for brake or turn signals. If one of the turn signal lights are working the unit is ok as the one unit works front and rear lights , left and right changed by the driver operated switch. With a vault meter check voltage at light socket contact and light earth . a rusty bulb holder or a bad earth from light body to car body can cause this fault.
Check your brake light socket housing, for good connection.
Do you have a voltmeter? If so, turn on your right directional and your park lights, probe the socket. One side of the socket should be on all the time, the other should be pulsing on and off. If you don't have a voltmeter, you can use any 12 volt light bulb. Wrap a wire around the outside of the bulb (this side goes to ground). With another wire held on the base of the bulb, use the other end of the wire to probe the socket as before, one side of the socket should be on all the time, the other should be pulsing on and off. If there is no one pulse then you have an open in that line. If you do get a pulse then your bulb isn't reaching the base of the socket. You might try adding a bit of solder to the base of the bulb. Or as a last resort replace the bulb socket.
Good luck, I hope this helps
- On my 2001 Durango, the tail light bulbs were good, but one of the socket electrical (rounded metallic) contacts was not making physical contact with the bulb when the bulb was inserted. The tail light would work but not the brake light. The fix was to put a small bead of solder on the socket electrical contact, which raised it enough to make contact with the bottom of the bulb. (Apparently the light had slightly melted the plastic socket, causing the brake light signal contact to separate from the bulb contact.) There might be a similar issue with the blinker.
Faulty wiring or bulb holder check these first as the plastic holders can crack clean all terminals and check the earth wiring
Your brake I believe depends on a switch just behind your brake pedals (on the fuse box- look for indicators on which fuse is each light, function connected to as no car has a single fuse for all lights).
SOURCE: 2001 dodge neon tail lights inop
looking at your schematics and , you say tail lights don't work , you didn't mention if front parking lights and license plate lights are working , they all come from the same source , a black /yellow wire , a good clue if front work and rear don't , please advise .if fronts work then you have a open circuit somewhere between junction S118 (near breakout for left headlamp) and rear sockets.
SOURCE: 2004 dodge durango left rear taillight won't light
Check for a bad socket assembly. Look for burnt retainers inside the socket.
SOURCE: I have a 02 durango and the passenger side tail
had the same problem on my 02 the light sockets looked but when put new ones in problem solved
SOURCE: 2005 Dodge Durango, no brake
The brake lights and reverse lights are on different circuits with different triggers. Check any trailer connections you have connected or spliced in that could be leading to a short. Double check the light control switch. If you have no tail lights when the lights are on then the problem is most likely the light control switch.
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