Took 3 hours to do this thing! Getting the turn signal wire to come out was fairly difficult because the wire was thicker than for the side marker. I had to pry back the plastic tongue from the housing with a large screwdriver. I have yet to put it back in as I'm waiting for my LED setup to arrive, and want to test with everything easily accessible. Everything was fairly simple except for figuring out how to get the terminal out. I tried for at least 30 minutes with a pick and paperclip and could not find the locking tab until I googled pictures and got an idea of what I was looking for. I then used a needle to move the tab and got the terminal out. I didn't have much left to work with as far as wire, and had to trim off a fair bit of insulation. As it turns out, the heat shrink I have is also slightly large and wasn't a perfect fit, so I jammed the rubber piece overtop of it and used electrical tape. I can't be asked to make it perfect, but hopefully it lasts!
Once I had it all together, I checked resistance and it looked good. Then tried the parking lights and voila, fixed! Though the side marker still wasn't working on either side. I checked the terminals with my multimeter and saw the voltage spiking to turn the light on and off as it should. Replaced both bulbs and we're good to go!
Longer end of wire stripped:
Terminal wire and main wire soldered back together:
And she works!