Have you taken a multimeter and verified you're not getting power to the tail lights? I had a tail light go out, took out the bulb, noticed corrosion, checked with the multimeter (power=yes), replaced the bulb and it worked. My guess is you have a bad component (bulb, socket, ground, wire)
I just noticed after posting, you said you have signal and brake lights but no "tail" lights. Do you mean the lights work when you press on the brake pedal, but do not work when the headlights are on/running lights? Or are you referring to the ID/clearance lights?