In the off position, it will turn on the new socket that I just ran my
12/2 with. Of course the other light bulb is now off.

What gives?

http://imgur.com/yvmsf


Thanks for your effort, but, I'm not sure it "works". But I should have
a 3-way around, to see if that will work out.

And, I'll just keep screwing and unscrewing copper till it does.

Also, I'll answer this here as well, but, the box with existing light
fixture was "full up". I could either put a junction box right next to
it, but, instead chose to make the run back to the light switch.