Checking the circuit at the brake switch is where I recommend checking first. Here is the information from the service manual for testing the switch:
The brake lamp switch can be tested with an ohmmeter. The ohmmeter is used to check continuity between the pin terminals (Brake Lamp Switch Terminal Identification).
NOTE: Disconnect switch harness before testing switch continuity.
With switch plunger extended, attach test leads to pins 1 and 2. Replace switch if meter indicates no continuity.
With switch plunger retracted, attach test leads to pins 3 and 4. Replace switch if meter indicates no continuity.
With switch plunger retracted, attach test leads to pins 5 and 6. Replace switch if meter indicates no continuity.
As a reference.....terminal #6 on the brake pedal switch is the one next to the plunger.
The brake lamp switch is hard wired to the Center High Mount Stop Lamp (CHMSL) and also monitored by the Instrument Cluster for use by the brake lamp, speed control brake sensor circuits and electronic brake distribution (EBD). The brake lamp circuit is open until the plunger is depressed. The speed control and brake sensor circuits are closed until the plunger is depressed. When the brake lamp switch transitions, the CHMSL transitions and instrument cluster transmits a brake applied/released message on the bus. The Integrated Power Module (IPM) will then transition the brake lamps.
When the brake light switch is activated, the Powertrain Control Module (PCM) receives an input indicating that the brakes are being applied. After receiving this input, the PCM maintains idle speed to a scheduled rpm through control of the Idle Air Control (IAC) motor. The brake switch input is also used to disable vent and vacuum solenoid output signals to the speed control servo.
Vehicles equipped with the speed control option use a dual function brake lamp switch. The PCM monitors the state of the dual function brake lamp switch.
The brake switch is equipped with three sets of contacts, one normally open and the other two normally closed (brakes disengaged). The PCM sends a 12 volt signal to one of the normally closed contacts in the brake switch, which is returned to the PCM as a brake switch state signal. With the contacts closed, the 12 volt signal is pulled to ground causing the signal to go low. The low voltage signal, monitored by the PCM, indicates that the brakes are not applied. When the brakes are applied, the contacts open, causing the PCM's output brake signal to go high, disengaging the speed control, cutting off PCM power to the speed control solenoids.
The second set of normally closed contacts supplies 12 volts from the PCM any time speed control is turned on. Through the brake switch, voltage is routed to the speed control servo solenoids. The speed control solenoids (vacuum, vent and dump) are provided this voltage any time the speed control is ON and the brakes are disengaged.
When the driver applies the brakes, the contacts open and voltage is interrupted to the solenoids. The normally open contacts are fed battery voltage. When the brakes are applied, battery voltage is supplied to the brake lamps.
The brake lamp switch can only be adjusted once. That is at the initial installation of the switch. If the switch is not adjusted properly or has been removed, a new switch must be installed and adjusted.
If the third brake lamp works then the circuit for the brake switch will check okay. As it mentioned above.....the switch also sends the brake pedal switch to the cluster which then sends it to the integrated power module (fuse box under the hood) which then turns the bed mounted brake lamps on. The bed mounted brake lamps are wired directly to the integrated power module.
The most likely cause will be the integrated power module. To be 100% sure....a scanner will be needed that can access the integrated power module to see if any codes and also if the lights can be actuated.
The IPM has a computer mounted to it (FCM) and one of its design benefits is fuse less circuits. When a problem is detected it can turn the circuit off. To be sure a scanner will be needed. It takes a special scanner such as the factory scanner that the dealer has. Here are some related wiring diagrams:
Please for give me if I give you more info but the different year models have different systems. This is the older version with the seperate FCM that is mounted to it, newer year models have a fuse box/computer in one unit call the TIPM. All you can do at this point is follow the wiring back to the IPM to see if the FCM is sending out the bed mounted brake lamp voltage.
Here is the basic break down.......from the brake switch to the instrument cluster to the IPM then internally to the FCM and then out to the brake lamps unit mounted on the bed.
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The schematics I gave you are for your vehicle. They are directly from Dodge. You can check the signal from the brake switch to the cluster however the cluster sends a message over the communication circuit that you will not be able to see with a mutimeter. Then you can check the output from the FCM as soon in the previous wiring diagram. In the wiring diagram with the brake switch you will see a splice which is where the circuit branches out to other directions. That splice is S214. In this next diagram you will see the same splice S214 going to the cluster. This is the circuit I mentioned that goes from the brake switch to the cluster.
You would need to remove the cluster and gain access to the white and tan striped wire and see if 12 volts is present when the brake pedal is depressed. Up to this point you will be able to check it. When it goes from the cluster to the FCM it is all computer language on the communication ciruits (one module talking to another).
You have the wiring diagram already for the FCM to the taillamp. If the system was working properly then you would have 12 volts coming out of the FCM on dark green and white striped wire leading to the left rear taillamp.
Here is the pinout for the FCM :
Here is the connector C3 of the IPM where the signal from the FCM leaves the IPM leading out to the left rear brake lamp:
So you can check the beginning ( from switch to the cluster), you cant check the portion from the cluster to the FCM, and you can check the end which is from the FCM to the left rear brake lamp bulb.
There will be only so much that you can check with a multimeter or power probe.....sooner or later you will need the proper scanner.