I finally found civilization, Walmart and the internet. I bought a new plug for the trailer and started cutting up the old one. I found the green, yellow, brown and white wires I am used to, but there was also Black, red, and light blue. There was a handy hot wire (Black) right there, so I decided to test the other colors to see if they came out like I expected. They did not.
The PDF file you provided a link to looked right to me, but it had NOTHING TO DO with how the Airstream plug was wired.
Brown has always been running lights. It turned out to be the Right turn signal.
Green is usually the right turn signal. It turned out to be the running lights.
Yellow is usually the left turn signal. It turned out to be the Back Up Lights.
White is usually ground and it turned out to be the ground.
Black was the hot wire.
Light Blue was the breaks.
Red was the left turn signal.
It all works now. Ainít standardization great!