When braking, green turn signal lights up and right rear brake light does not come on. (have replaced brake light)

If both the brake lights and rear turn signals are not functioning in your 2008 Dodge Charger, there are several possible causes to consider. Here are some common issues that could lead to this problem:
1. Blown fuses: Check the fuse box for any blown fuses related to the brake lights and turn signals. A blown fuse can interrupt the circuit and prevent the lights from working. Refer to your vehicle's manual to locate the specific fuse for these functions and replace it if necessary.
2. Faulty bulbs: Inspect the bulbs in the brake lights and turn signals to see if they are burnt out or damaged. If a bulb is not working, it should be replaced. It's possible that multiple bulbs have failed simultaneously, leading to both the brake lights and turn signals not functioning.
3. Wiring issues: Check the wiring connections and harnesses for any signs of damage, loose connections, or corrosion. Faulty wiring can disrupt the electrical flow and prevent the lights from operating. Repair or replace any damaged wiring as needed.
4. Malfunctioning brake light switch: The brake light switch, located near the brake pedal, activates the brake lights when the pedal is pressed. If the switch is faulty or misaligned, it can cause the brake lights to not work. Consider having the brake light switch inspected and replaced if necessary.
5. Faulty turn signal relay: The turn signal relay controls the flashing of the turn signals. If the relay is defective, it can prevent the rear turn signals from operating. Consider replacing the turn signal relay if other potential causes have been ruled out.
If troubleshooting these common issues does not resolve the problem, it is recommended to consult a professional mechanic or authorized Dodge service center for a more accurate diagnosis and repair. They will have the expertise and necessary tools to pinpoint and fix the specific issue with your 2008 Dodge Charger's brake lights and rear turn signals.

check to see if the wire connector is plugged in properly

sounds like a crossed wire , I saw problems with the brake light switch that is located on the brake pedal

The Left Turn signal is DARK GREEN/RED
The Right Turn signal is WHITE/YELLOW
The Left Brake light is WHITE/ORANGE
The Right Brake is WHITE/RED
The High-Mount Brake lamp is DARK GREEN/WHITE

Now, with all that said, your Jeep should be already equipped with trailer wiring unless you have the cheapest model of Jeep Liberty available. I would check your Owner's Manual on the subject.

Also, your rear lighting is controlled by the Body Control Module (BCM) and the signal and brake inputs/outputs are all transmitted to the Instrument Cluster Module for your lamp-out warning system. Anything you connect to this wiring can adversely affect BCM function or can cause your lamp out warning to malfunction and come on all the time. I would use extreme caution unless you really want to destroy some HIGH DOLLAR electronics in your vehicle.

The flasher does not stop the brake lights from working. Check # 18 fuse in fusebox under lower left side of dash. if it's ok, the brake light switch, on the brake pedal arm is next. light green wire with red stripe is hot if fuse 18 is ok. Depress brake pedal, light green with no stripe should have power. if not, replace brake light switch. If light green wire has power with pedal depressed, combination switch under the steering is next. Remove the cover from around the combo switch {under the steering wheel}. depress brake pedal, light green wire should have power. If it does, pedal still depressed, orange with light blue wire & wire with light green & orange should have power. Those 2 wires are brake & rear turn signal wires. { The turn signal switch should be in the middle, not right position or left. while checking for power in the last 2 wires. Good Luck drvolt.

should be green and yellow...brown is park lights

Check for power at the turn signal switch. White wire comes from brake switch switch into the turn signal switch. The brake light switch is working because the high mount brake light is working..right? Do the turn signals work ok? if so, then the wiring is OK. The brake signal wires that come out of the turn signal switch are dark green(right) and yellow (left).

Sound's like their is a problem with the right hand rear light cluster.The reason it only happen's going down a hill is you applying the brake. The only place the brake and indicator light's come together is the rear clusted. To check this apply the hand brake gently with the button held in instead of useing the foot brake. This may not be the fault but it is worth a try as it seems the most likely problem.

have you checked the earthing continuity-if it's this other bulbs may also partly light when brakes used
otherwise-
Check continuity of live from center to lh & rh lights and/or is there a live at those lights

Rear lights are double filament bulbs one side for the lights other side for the brake/turn signals so it still may be a bulb. Do u have a test light or volt meter you can check to make sure u have power there when brakes or turn signals are activated. Or just try another bulb.