2000 chevy silverado tail lights don't work but 3rd brake light work when applying brakes. While night driving both of the rear singal lights will glow but the running lights wont work until i press the brake pedal. I can tell when its doing this because the signal lights on the dash will iluminate.

Check the switch that is under the dash on the brake pedal arm.

The tail light fuse is under the rear seat on the drivers side.

If after checking the bulbs are ok then the fuses could be suspect!

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Did you check the park fuses, note the diagram, rr and lr. Use a test light to check voltage at fuse circuit, headlamp switch on. That should tell us if problem is before the fuse or after.
You always want to check voltage and ground circuits, for lamps. Do the front park lamps work?

tail lights not working

This will either be a fuse or the brake light switch which is on the pedal it's self. More likely the switch as these are fickle at best.

Power for left rear turn signal is dark blue
Power for left rear tail light is brown
Power for left rear stop light is light blue.
Black is ground

I've worked on these the first drove me crazy. its the turn signal switch every thing runs thru these. head lights, turn signal, brakes. except the third brake light. it runs directly from the brake switch. go figuare

sounds like it may be a faulty brake switch.

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