Drivers running light out 2005 express 2500

SOURCE: license plate lights do not work after replacing both of them

They are on the same electrical circuit as your marker lights. You could have a bad ground at the license plate area.

SOURCE: License Plate lights won't work

first of all i would get a 12- volt tested and turn the lights on take the new blub out and then test the sockets and no power test the wires behind the sockets if you have power then the sockets are bad or burn out replace if needed.

SOURCE: license plate light replacement

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.

SOURCE: check engine light flashing

if it shaking it could be suspension. tires bent axel and rim. but that wouldnt cause to lose power...
fuel air spark ratio isnt right. that is just what it sounds like.
ignition time could be off.
in proper fuel adjestment in the carb/ or if fuel injected..
thats a breif idea of what i got from it..

SOURCE: changing license plate lights on 2004 chevrolet

the light can be replaced from the back side of the light housing . go under the back side of bumper under the truck behind lisence plate you will see the where the wire goes to the light . grab the housing not the wires and twist about a half a turn and pull gently. it should come out and then remove the light bulb and replace with new