Replace the license plate light on a 2002 lincoln LS

License Plate Lamp Removal and Installation

1. If necessary, remove the license plate.

1. Remove the pin-type retainers and the luggage compartment lid trim panel.

1. Disconnect the license plate lamp electrical connector.

1. Remove the lamp socket from the license plate lamp.

1. Using a suitable tool, through the access hole, release the clips and remove the license plate lamp.

check your owners manual should be info of location of fuse .

follow this link but it looks like what you have described ,may just need a shove
Battery Replacement 2000 2002 Lincoln LS 2000 Lincoln LS 3 0L V6

Sounds like either your wiring from the Light switch is bad or the Light switch itself is bad. Check with your Owners manual to see if the "Parking lights" have a separate fuse.

Your tail and License plate lights would light with either the Headlights or the "Parking" light selected at the switch as would the front parking lights. If all lights except the headlights are out, your problem is closer to the light switch than at the mounting points of each Parking light or License plate light.

This is one case where you will not know if a dead wire off of the switch is dead because of a bad switch or a bad wire. You would have to detach the harness at the switch, test the wire bundle or jump the switch with power to see how it distributes power through the Harness. It will take a lot of time to rule out the switch. It may be cheaper to replace the switch and then work from there.

Open Trunk

Pull back trunk liner

Remove 3 nuts holding
tail light housing on

Pull housing away from body & replace bulb

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

check your transmission checked

The license plate lights are in the ledge above the license plate. 2 screws keep the lens cover in place. Remove the screws, and the cover comes off. Just pull the lamp out (wedge base) and replace.

you have to carefully pry the bulb holder out and remove the bulb by turning it counterclockwise while pushing in. Replace the new lightbulb the reverse mode.