Be sure the master switch is not turned off. Consult the owners manual.
Put the dome light switch on door located on the headliner to the side of the light
Most likely the fuse is blown for the dome light on the Silverado if the light doesn't come on.
If you push that button, the dome light inside of the truck won't come on when you open the door.
The dome light switch has 3 positions. Off-On-On when the door is opened. Put it in the proper position.
The bulb could be blown.
By pass the door mode. The Dome light should have a 3 way switch OFF - Door open on - Constant on Move the switch to the off mode, and light should not come on when door is opened.
is the switch on the dome light set to doors! if so, one of the door switches are stuck. spray all door switches with a good lubricating spray. and push on buttons with hand to free them up. if not that, then one of the door switches are bad. or the dome light bulb is burnt out.
The dome light switch on the dash is on.
Bad bulb, check fuse if other courtesy lights out or if the only one
Take the bulb out.
check your relays
check the drivers door jam area you should see a little tab sticking out it pushes in and out when opening and closing the door that triggers the light