In short, my right rear turn signal crapped out. I've replaced the bulb and the fuse is fine. So my next question is will a bad flasher relay cause one signal light to not work? Also, before it stopped working all together, it would switch between flashing fast and flashing normal for a few seconds before it stopped working all together. (2002 Sunfire).

Gotta be a wiring issue. Check for power at the plug... and trace wires

I'm going to guess it's going to be the plug itself. Get a multimeter out and start testing.