Chevy provides you with a fuse puller tool inside the driver side instrument fuse block.
2006 chevy silverado brake light fuse location.
Lift the cover for access to the fuse relay block.
Since the center mount brake light works when the pedal is pressed it appears that the brake switch is not the issue.
Then check the brake light switch on the bake pedal arm.
I checked every fuse in both boxes and all four bulbs and they all appear fine.
For chevrolet silverado first generation 1999 2000 2001 2002 2003 2004 2005 2007 model year.
Open the driver side door and pull the cover off the fuse block to access the puller.
Fuse box in engine compartment.
2006 chevrolet silverado 2500hd tail lights stopped working i am having the same problem on an 04 2500hd there isa 15 amp stop light fuse inside the cab on the side of the instrument panel and a 25 amp stop light fuse under hood.
The bed brake lights are not working but all other lights including the center mount brake light are working fine.
You can remove fuses with a fuse extractor.
In the instrument panel on the side of the dash you should see rt trlr st trn for trailer right turn and brake signal and lt trlr st trn for trailer left turn and brake lights.
Back probe the switch terminals with a test light.
The fuse extractor is located in the underhood electrical center.
Only one of the switch terminals should turn on the test light.
From what i was able to find there are several fuses associated with the tow package wiring on a 2006 chevy silverado.