the chart in the link is the correct setup. i don't think that you'll get much of a better connection by soldering the wires. a wire harness shouldn't run you more than $15 CAD. save yourself the time and energy and just get the harness. just match up the colors of the harness to your new deck... then plug the harness into your Toyota plug. done!
on the left you'll see the harness plugged into the Toyota plug. all that's left is match up the harness colors to the deck colors.
EDIT: also, if you ever want to switch you deck again in the future... it's a much easier and neater job to do.
-rayray