I admire your analytical view of this third light problem. You must have been an engineer or technician in your professional life.

About the rear defogger repair, I went through this many times since the previous owner had the VERY bad habit of using the hand ice/snow scraper also inside the car. Some wires have been weakened.

I used Permatex rear window defogger repair kit with success. It cost about $8 here last time I purcased it. One thing is that once opened the tiny bottle tend to loose its solvent. And the conductive powder in suspension solidifies.

But I cheat and re-fluidize it. I use a few drops of acetone, lacquer thinner (toluene is better I would think) and grind the lumps until the mixture is fine paste. Then I use it and apply double coats on the broken defogger wire.

Works well for me.