Why doesn't right tail light work when the lights are on but works when the key fob is used to lock or unlock the truck?

REAR 3rd lamp (is inner) sure.. exterior rear 3rd.
A USA car right, wiring not the same outside, so.....nor canada.
Well yoiutube is wrong, as most are.
using voltmeter finds out if (inner = 3rd rear brake) lamp power feed is dead or ground bad. its just 2 wires. there. (a 2 man test)
or bad BCM (not this time)
they also didn't tell you the service manual covers this.
USA F13 runs all 3 brake lamps just 1 wire to the rear. from foot switch. brake.
right and high (3rd center use on ground G701

.here is the USA brake wiring, nobody on yourtube knows.
only one fuse F13 and NO BCM here.
12vdc is top at pin A9, brakes on
and connects to all 3 lamps see # 2 others.
then 7 connections to fail.
12vdc to lamp pin1 if not then back up to next connector
if 12vdc is at lamp pin2 ground is bad.(broken)
just 2 tests and 1/2 the cause is known, at the lamp socket
pin 1.ad 2.
pin1,12vdc foot on brake
pin 2,0vdc foot on brake

To arm content theft alarm.
1. Open the door.
2. Lock the door with the power door lock switch or
the remote keyless entry transmitter. The
SECURITY light should flash.
3. Close all doors. The SECURITY light should go off
after approximately 30 seconds. The alarm is not
armed until the SECURITY light goes off.

If a locked door is opened without the key or the remote keyless entry transmitter, the alarm will go off. The headlamps and parking lamps will flash for two minutes, and the horn will sound for 30 seconds, then will turn off to save the battery power.

Use the key not the fob on the drivers door. Lock it and unlock it. If you have another factory key try it also.

I had a problem where my key fob did not lock or unlock the car, Renault Clio Dynamique, but the central locking button in the car did still work and engine turned over fine. Changed the key fob battery still nothing. Read online about disconnecting and reconnecting the car battery, (negative only) and hey presto it worked! All working fine now!

Yes it is,the drive door actuator being non op

1) Try the other fob.
2) Driver door latch mechanism needs repair/replacement.

There is a harness that you unplugged for the rear tail lamp. Make sure it is fully pressed and locked. This is always the cause on jags for tail lamp failure.

These issues have all the symptoms of a failing CTM or Central Timing Module. The unit is located behind the kick panel down by the drivers feet.

The part installed is ~$450-500 bucks at your local dealer. They will need all your remote fobs as they must be relearned into the new CTM.

The horn chirp can be disable by pressing the lock and unlock buttons simultaneously until the hazard lights flash, and no enable press the lock and unlock until the horn chirp.
To reprogram (enter new ID) key fob (keyless remote controller) follow the steps.
1. Close all doors and lock all doors
2. Insert and remove the key from the ignition key cylinder more than six times within 10 seconds. (The hazard warning lamp will then flash.) NOTE: Key should be withdrawn from ignition key cylinder completely each time.
NOTE: Do not rush the insertion/removal key cycling process. The side marker/tail/license lamps and interior illumination will flash twice when this step is accurately completed.
3. Insert key on ignition key cylinder and turn ignition key switch to "AAC" position At this time, the new ID code is entered and original (previous) ID codes are erase.
4. Press any button on the new remote controller once. (The hazard warning lamp will then flash)
NOTE: Do not press the button more than one time in the above step. If the button is pressed more than one time, the programming procedure will not be successful. The side marker/tail/license lamps and interior illumination will flash twice when this step is accurately completed and programming is successful.
If there is only one remote controller skip step 5.
5. Additional ID code entry Release the door lock, then lock again with door lock/unlock switch (In power window main switch)
6. Remove key from ignition
7. Unlock driver side door, open driver side door and then close the door. (END)

If it is a 2003 model year vehicle follow this procedure. If it doesn't work, you may have the wrong fob which happens all the time.

Sit in vehicle and close all doors.
COMPLETELY insert and remove ignition key more than six times within 10 seconds.
Hazard lights should flash twice.
Turn ignition to ACC position
Press and hold any button on the new key fob hazard lights will flash twice
For a second key fob using the master lock switch, lock and unlock the doors then hold down any button on the second remote until the hazard lamps flash twice.
Then you are done open the door to exit the programming mode.
If the lamps didn't flash when holding down the key fob make sure you have the right key fob, they are different for each car.