My driver rear running light went out but it's not the bulb or the socket. I've replaced both. Brake light (from the same bulb (3047)) comes on fine, but the running light won't come on no matter what. Any idea? (2005 4.7 4x4)

 

I've tried both 3157 and 3057 bulbs with no luck

 

Any stored codes, it would be a code numbered B16xx, and would not trigger a CEL.

It could be a wiring / ground issue.

Here is some info from the FSM about the parking lamps.

OPERATION
Following are paragraphs that briefly describe the operation of each of the major exterior lighting systems. The hard wired circuits and components of the exterior lighting systems may be diagnosed and tested using conventional diagnostic tools and procedures. Refer to the appropriate wiring information.

However, conventional diagnostic methods may not prove conclusive in the diagnosis of the ElectroMechanical
Instrument Cluster (EMIC) (also known as the Cab Control Node/CCN), the Front Control Module (FCM) (also
known as the Integrated Power Module/IPM), the Powertrain Control Module (PCM) or the Controller Area Network (CAN) data bus. The most reliable, efficient, and accurate means to diagnose the EMIC, the FCM, the PCM, the CAN data bus or the electronic bus message inputs and outputs related to the various exterior lighting systems requires the use of a diagnostic scan tool. Refer to the appropriate diagnostic information.

PARK LAMPS
The park lamps system includes the EMIC, the FCM, a park lamp relay installed in the PDC, and the headlamp
switch on the instrument panel. The front park lamp and side marker lamp bulbs each have a path to ground at all
times through their connection to the headlamp and dash wire harness. The headlamp and dash wire harness has
takeouts with eyelet terminals that are secured by ground screws to the right (right park lamp and side marker lamp bulbs) and left (left park lamp and side marker lamp bulbs) inboard sides of the hydroform within the engine compartment.

The rear park lamp, side marker lamp and license plate lamp bulbs have a path to ground at all times
through a takeout and eyelet terminal of the left headlamp and dash wire harness that is secured by a ground screw to the left inboard side of the hydroform within the engine compartment.

The EMIC monitors a hard wired multiplex input from the headlamp switch, then sends the appropriate electronic
headlamp switch status messages to the FCM over the CAN data bus. The FCM responds to these messages by
energizing or de-energizing the park lamp relay. When the park lamp relay is energized, it provides battery voltage
from a fuse in the PDC through a park lamp relay output circuit to the appropriate lamp bulbs. The FCM provides
a battery saver (load shedding) feature for the park lamps, which will turn these lamps off if they are left on for more than about eight minutes with the ignition switch in the Lock position. The EMIC provides a fail-safe feature for the park lamps, which will send an electronic message to the FCM to turn these lamps on automatically if it detects no input from the headlamp switch.

Park Lamp Relay - A park lamp relay is located in the Power Distribution Center (PDC) of all vehicles.

 

forward control module has crapped out due to rust or contamination, happen to my truck, had to jump wires from one brake light to another