Not sure if OP has solved the issue of rear blinkers and taillights not working, but has anyone considered the turn signal switch? I know in my Vette I had an issue where the rear right taillights wouldn't brighten either when braking or signaling but would illuminate when the headlights or running lights were on. As it turns out, the wires to the brake lights and the turn signals all ran through the same switch, so when the switch failed, those lights wouldn't light up for braking or signaling. Not sure if GM did the same here, there's about a 13-year difference between the two, but figured it worth mentioning. Replace your bulbs, then check to make sure you're getting power to those lights when braking or blinking while you're back there(check at the socket and the connector, would hate for you to go through all that trouble just to find that it's a bad socket). If you aren't, check your fuses; if you are at both socket and connector, clean off the contacts in the socket; if you are at the connector but not the socket, then you've probably found what needs replacing. If the fuse(s) are good, check that the relay(s) are functioning and that they are receiving power. Don't know how much more I can accurately say on the topic, the last car I did this on was made in 94 so the wiring was a bit simpler. Hope you figure out what's causing it!
~Ken
~Ken