That's exactly what I was doing! Here's how I got to my original question: clearly something is wrong here but I don't see it. Hopefully you do.
If I draw a straight line from "X" to "Y" and continue around the globe, that line will pass thru the south pole and eventually connect back to "X", making a complete circle around the globe. In doing so I have drawn 2 lines of longitude that are 180° apart.
Then if I put a dot "Z" anywhere on that line by definition "X", "Y", and "Z" will be in perfect alignment. In my mind no matter where on that line I put "Z" the declination should be 0°. (Why isn't it?)
AlbaNY_Ram