Backup light turn signals and backup lights stopped working

Tail lights typically use the chassis (ground) for the circuit return path. Are all tail lights out or just the brake lights?

If rear brake, turn signal, and backup lights are out then likely a ground has failed.

If rear turn signal and hazard lights work amd only the brakes not working then it's more likely a control device (brake switch, etc.)

Signal lights and backup lights are generally on two completely different circuits. Check your fuses first.

https://www.fiatusa.com/download/pdf/manuals/2014-FIAT-500L-OM-1st.pdf

it's in your owners manual page 358 chapter 7

you need a torx 20 screwdriver or bit

Rear Tail, Stop, Backup And Turn Signal Lamps
1. Open the liftgate.
2. Remove the two screws and remove the tail lamp assembly.
3. Remove the four screws (using a T20 driver) and separate the backplate from the lamp housing.
4. Remove the tail, stop, or turn signal bulbs by pushing them slightly and turning counter-clockwise.
5. Remove the backup lamp bulb by pulling straight out.
6. Replace lamps as required and reinstall lamp.

Center High-Mounted Stop Lamp (CHMSL)
This light is an LED assembly. See your authorized stealership

Usually if you turn on your turn signal and it stays lit solid inside, it's telling you the bulb is bad in your turn signal outside. I would check your bulbs first. Same for the backup lights.

Lighting control module ? ?????? Hazard / flasher module ! Now ( there''s not even an electrical signal where the fuse plugs into the interior fuse panel.) What FUSE ??????

Stop Lamps
The STOP LP 25 A fuse in the underhood fuse block supplies battery positive voltage to the normally open stop lamp switch. When the driver presses the brake pedal, the switch contacts close and battery positive voltage is supplied to both the STOP 15 A fuse and the CHMSL 10 A fuse in the I/P fuse block, and to the turn signal/hazard module. The turn signal/hazard module then supplies voltage to both of the trailer rear turn/stop lamp supply voltage circuits. The voltage from the CHMSL 10 A fuse is to the center high mounted stop lamp (CHMSL) and the trailer jumper harness. The voltage from the STOP 15 A fuse is to the stop lamps, throttle actuator control (TAC) module, and the cruise control.
Backup Lamps
The backup lamp request signal is sent from the powertrain control module (PCM) to the body control module (BCM) on the Class 2 message system. This signal is based on the park neutral position (PNP) switch signal. The BCM supplies voltage on the backup lamp supply voltage circuit to the backup lamps and to the automatic day/night mirror. Voltage for the courtesy lamp supply voltage circuit and backup lamp supply voltage circuit is from the TBC B fuse in the instrument panel fuse block directly through the BCM to these circuits. A short to ground on either of these circuits will open the fuse. The backup lamps are grounded at G401.
For trailer wiring, a separate backup lamp circuit is connected through the underhood fuse block from the TRLR B/U 10 A fuse to the trailer wiring harness.
Turn Signal/Hazard Lamps
The IGN E 10 A fuse in the underhood fuse block supplies battery positive voltage to the turn signal/hazard switch assembly. The FLASH 25 A fuse in the I/P fuse block supplies battery positive voltage to the turn signal/flasher module and ground is supplied at G200. When the turn signal switch is placed in either the left or right position, a voltage signal is completed from the turn signal switch to the turn sign/flasher module. When the hazard flasher switch is activated, a ground signal is completed from the turn signal/hazard switch to the turn sign/flasher module. The turn sign/flasher module then sends an on-off voltage signal through the LT TRLR, RT TRLR, LT TURN or RT TURN 10 A fuses in the I/P fuse block to the appropriate turn signal or to all 4 fuses for hazard operation. The instrument panel cluster (IPC) indicators receive voltage from the LT TURN and RT TURN fuses as well as the DDM/PDM for the mirror turn signals. The DDM/PDM has no function or control of the mirror turn signals other that a pass through connection for the circuits. The audio chime is also activated when the turn signals are on. When the hazard switch is pressed, all turn signal lamps will flash including both IPC turn indicators. The front turn signals are grounded at G100. The rear turn signals are grounded at G401. The Mirror turn signals are grounded by the DDM/PDM.

Do you know how to do automotive electrical circuit testing with a test light or volt meter ? How to read an use a wiring diagram to pin point testing points . ( connectors , fuse locations etc... ) How to use a power flow chart ? Here is a site for just such info .

http://www.bbbind.com/free_tsb.html Enter vehicle info . year , make , model an engine size . System click lighting , subsystem exterior lighting . Second diagram shows trailer wiring .
Electric Testing Techniques You Need to Know

Mastering Voltage Drop Testing with Pete Meier and Jerry Truglia

CHEVROLET 2007 SILVERADO TRAILER LIGHT TROUBLESHOOTING

CHECK ALL BULBS IF BULBS OKAY,REASON REVERSE LIGHTS DONT WORK YOU HAVE FAULTY INHIBITOR SWITCH.FOR BRAKE LIGHTS NOT TO WORK,EITHER BRAKE LIGHT SWITCH FAULTY OR TURN SIGNAL BAD,BECAUSE MOST CARS NOW TURN SIGNAL SWITCH AND BRAKE LIGHTS SHARE SAME CIRCUIT.

It all depent's which ones are out, here a list of rear bulb's.

Turn signal bulbs # 921
Stoplight's # 3057
Tail light's # 3057
Backup light's # 921
Center stop light # 921
License plate light # 17177
Side marker # 194

Have some one turn light on while some one check them. First light then brakes then turn signals. till you see which ones don't work, and replace as needed.

One of 2 things to have checked, if all your bulbs and connections are correct. 1-stop lamp switch module.
2-multifunction/combination switch (blinker arm/components that are in the steering column). For about a 1/2 hrs. labor cost, a mechanic should be able to test the circuits.

Reconnecting a 7 wire circuit.....I presume you have located the rear JUNCTION BOX, or HARNESS splice.... At the lights wiring.
1. YELLOW = LH Turn signal
2. RED= STOP Lights
3. WHITE= Ground
4. BLACK= LH Tail Light/# plate lamp
5. BLUE [If available] Auxiliary Power Supply
6. GREEN= RH Turn signal
7.BROWN=RH Tail Lights
Depending on style you may find that the LH and RH Tail lamp colours are the same.[ie] Both Brown or both Black.
Best of luck in your endevours.
Regards DT

check for blown fuse(s). Seems like you tapped into the backup light circuit.