OK, I got this done and the headlight is working perfectly now. My attempt at doing the soldering was ugly, and I could not slide the heat shrink sleeves back over the twisted pairs. I used electrical tape around each pair, then bundled the 3 pairs with more electrical tape before taping the flex tubing around the bundle.
It needs to be noted that about a year ago, I noticed that this headlight had a good quantity of water in it. I drilled a small hole in the bottom of the lens to drain the water out, but even today, there is still condensation inside. I have two replacement headlamp assemblies for this vehicle, but even after looking at the manual, am confused about how to put change them out. Also, every time I mess with the black retainer rings that hold the bulb and connector in the socket, I break a piece of plastic off of the ring. If anyone knows of where I could buy these retainer rings I would be grateful to hear about it. Also, if there is any quick advice about changing out the headlight assemblies, I would be grateful to hear that too. Pedro, thank you again. Your precise instructions were perfect for a sometimes reluctant do-it-yourselfer like me.