License plate light out

Question edited for clarity.
Question moved to model category.

Check where the earth from those lights meets the bodywork.

It is a known issue

https://www.google.com/search?q=2003+Buick+Century.+My+license+plate+bulb+not+working

Fuse 4 does the cigarette light and the side mirrors. Do the mirrors work?
4 15A Cigarette lighter and control system for side mirrors


Fuse 6 does tail lights
6 15A Stop lights
Fuse 14 does the Dash Lights
14 10A Interior lighting and luggage. compartments, clock, radio or radio tape recorder, instrument cluster, central door lock control unit, engine control unit, automatic transmission control unit
If all those fuses are okay, you need a good auto-electrician.

https://fuseandrelay.com/mitsubishi/mirage.html

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Do the park lamps work ? license plate lights get power from same fuse ! Check ground wire ! use a volt meter an do voltage drop test ! Voltage Drop Testing The fuse for the license plate lights is in the under hood fuse box -engine compartment ! fuse #12 RT PRK LAMP 10Amp .

There's a fuse box behind tyhe glove compartment. You should have access to it when you open the glove compartment. Then there is also the fuse box in the engine compartment, that is next to the windshield wiper fluid on the passenger side. When my side marker lights and license plate light went out, I had to change
a fuse in the fuse box in the engine compartment. Hope this helps

When you are talking about "indicators" we could assuming that your are refer about signal lights. This work with "flashers" devices.

For 1996 Audi A4 2.8L SFI 6cyl the Flasher is located in front seating area, driver side, under dash, behind dash lower panel, mounted above driver side of steering column.

About generic fuses, open the driver side door. Remove panel on left side of dash. Fuse box is behind panel:

Fuse # / Description / Amps
1 / Heated washer jets / 5
2 / Turn signals flasher unit / 10
3 / Headlight washer, illumination of glove compartment, engine compartment, climate control, automatic transmission, instrument cluster / 5
4 / License plate light / 5
5 / Instrument cluster, seat heating, test connection for cruise control, bulb monitor for auto-check control, Automatic transmission display, switch lighting, mirror switches and actuators, airbag warning light, outside temperature indicator, Climate control / 10
6 / Central locking system / 5
7 / Anti-lock brake system / 10
8 / Vacant
9 / Mirror heating / 10
10 / Vacant
11 / Cruise control (automatic transmission) / 5
12 / On board diagnostic system / 10
13 / Brake lights / 10
14 / Interior lights, reading lights, anti-theft alarm system, vanity mirror / 10
15 / Instrument cluster, power windows, climate control, automatic transmission / 10
16 / Anti-lock brake system, Anti-Slip-Regulation / 5
17 / Heated door locks / 10
18 / High beam right / 10
19 / High beam left / 10
20 / Low beam right / 15
21 / Low beam left / 15
22 / Tail and side marker right / 5
23 / Tail and side marker left / 5
24 / Wiper and washer system / 25
25 / Blower for heating, climate control / 30
26 / Rear window defogger, mirror heating / 30
27 / Rear window wiper / 15
28 / Fuel pump / 15
29 / Engine timing / 20
30 / Sun roof / 20
31 / Tail lights, cruise control, automatic transmission / 15
32 / Engine timing / 20
33 / Cigarette lighter / 15
34 / Engine timing / 15
35 / Trailer receptacle / 30
36 / Fog lights / 15
37 / Radio / 20
38 / Luggage compartment light, central locking system / 15
39 / Emergency flasher / 15
40 / Horn / 25
41 / Anti-lock brake system / 25
42 / Vacant
43 / Vacant
44 / Seat heating / 30

Hope this helps (remember to rate and comme this free answeer).

First, your instrument panel lights. Make sure to check the knob on the dashboard to the left of the instrument panel which controls
the brightness of the instrument panel lights. Push the knob to get it to pop out. Turn the knob to adjust the brightness.
If that is not the problem, go to your fuse boxes. Check those in the interior fuse box (left kick panel, below the dash--fuse chart on the cover) and those in the engine compartment fuse box (far upper left as you face the car). If, after you replace anything that has blown, it blows again, that would suggest a short somewhere in the system.
If you don't find any blown fuses (and I think you will) then it's time to go to the light bulbs. The tail light bulbs are accessed from inside the trunk. The license plate bulbs are just above the license plate and are accessed by removing two screws that hold the fixture in, then taking off the click plate and removing the bulbs.
Hope this is of some help.

License Plate Lights Removal & Installation License plate lamp retainer clips

To Remove:
Remove or disconnect the following:

1. License plate
2. Pin-type retainers and the luggage compartment lid trim panel
3. License plate lamp electrical connector
4. Lamp socket from the license plate lamp
5. Using a suitable tool, through the access hole, release the clips and remove the license plate lamp

To Install:

1. Install or connect the following:
2. License plate lamp
3. Lamp socket to the license plate lamp
4. Electrical connector
5. Luggage compartment lid trim panel
6. License plate

change the bulb in the tail light. And check your fuses for the license plate.

this is straight out of the book ok

1. Open the rear compartment lid.
2. Remove the rear compartment lid trim.
3. Pull back on the rear compartment trim panel.
4. Unplug the lamp connector from the rear compartment lid wiring harness.
5. Press the grommet out of the rear compartment lid.
6. Remove the nuts retaining the lamp assembly to the rear compartment lid.
7. Remove the bulb.

it is most likley a wiring problem or the corosion, the license plate lights are tied to the tail lights.