Replacing rear turn signal bulb in 2003 Mustang

Did you replace the bulb in the passenger side running light/turn signal socket? There are two filaments in that bulb, one for the running light (which you indicate works) and one for the turn signal. If that bulb (filament) is burned out, it will make the turn signal flash faster. I don't know why you were swapping headlights, don't know where the fire box under the hood is, and don't know what a jumper sore is, so can't help you any further. I have a Saturn Ion, and have never found a fire box or jumper sore in it.

drop the tailgate and access the screws for the taillights, 150 LED Tail Light Rear Turn Signal Bulb Red Pair 1997 2016 Raptor 2010...

Dear Alex,
The problem is in the bulb, or the socket, or the wiring to these.
Whenever a turn signal flashes fast, know that one of the bulbs is not working.
You have already identified the problem as being the front one. Problem could be the hot wire, or the ground wire, or the ground connection to this bulb.
Start by taking a tester to the hot wire, and see if it is receiving electrical impulses when the turn signal is on.
( It probably is, unless the car has been in a wreck and has been improperly repaired.)
Then check the socket or the wires to is and see if the bulb is grounded.
I suspect the ground is defective, and either a new socket or a repair to the ground wire should fix you rights up.
God bless your efforts.

Check the wiring to the bulb. There may be a broke wire shorting out.

No, because the left side is still working. The loose wiring was to the multifunction switch (turn signal).

Power gores through the turn signal switch to the brake switch on the brake pedal, then to the rear lights. Does the highmount brake lamp work?
At the RH lamp socket, Measure the voltage between the RH rear lamp C4032 pin 3, circuit 5 (OG/LB), harness side and ground. Should be 12 volts.

try that first.

Did you change the front and rear bulbs?

There is an access panel on the inside rear sides by the lift gate. They pop out giving you access to the bulbs. I recommend replacing both at the same time since they seem to "blow" within a few days of each other.

First,

1. Turn the engine off and open the hood. Pry up the two fasteners from the radiator air baffle with a flat head screwdriver. Move the baffle to the side to access the top of the headlight case.
   
2. Step 2 Pull up the two metal rods behind the headlight case. These secure the case to the car. You may need your pliers to pull them up.
   
3. Step 3 Gently pull the headlight case out to access its rear. On the rear, you will find several black dust covers. Twist off the dust cover closest to the fender (the outward dust cover) to access the turn signal bulb.
   
4. Step 4 Turn the bulb module counterclockwise to release it. Unplug the electrical connector from the bulb module. Connect the new bulb to the electrical connector (don't touch the glass with your hands; hold it by the plastic piece). Insert the bulb module in the turn signal housing, turn it clockwise and screw the dust cover back on.
   
5. Step 5 Insert the headlight case in the mount. Push the pins back down to secure it. Position the radiator baffle in its place and insert the fasteners.
   
Rear Turn Signal Bulbs
6. Step 1 Open the trunk. Remove the net from the side mounted wing nut (on the side with the faulty turn signal). Twist the wing nuts (there are two per side) counterclockwise to remove them.
   
7. Step 2 Peel the carpet layer back to access the rear signal lamp wing nuts. Twist these wing nuts (two per side) counterclockwise to remove them and release the rear signal.
   
8. Step 3 Carefully pull the rear signal assembly away from the Impala. The rear turn signal is the inner bulb (closest to the trunk). Press the tab on the bulb module and turn it counterclockwise to release it from the rear signal assembly.
   
9. Step 4 Pull the old bulb straight off the module (don't twist). Insert the new bulb in the module. Depress the tab on the connection and insert the module back in the assembly. Twist it clockwise.
   
10. Step 5 Insert the rear signal assembly. Re-attach the assembly's wing nuts and push the carpet layer back in place. Tighten the other two wing nuts to secure the carpet layer and reconnect the cargo net
    

make sure your tire is ok and is not r ubbing on anything and check your drivetrain ujoint`s etc.

Are the rear bulbs OK?
Is the ground good at the rear?are the sockets good?
Are there tail lights and a license plate light?then the ground is OK.
All the things that you say do not work go through the signal light switch....it may need replacing.
First make sure the bulbs and fuses are OK and power is getting to the signal light switch and to the brake light switch.
Nice car!

at the very rear ... it would be changed from within the trunk... the side bulb would be changed from inside the trunk or underneath behind the sheet metal

Robert