I found the following quote on another Tundra Forum. Does this sound like the wire you have left over? -- By the way, I have not idea if the instructions below are correct; so take it with a grain of salt. However, the explanation sounds logical.
"The one thing you do need to pay attention to is that the Tundra tow plug in the kick panel will not supply a proper ground. Tekonsha fixed this problem by adding a second ground wire (White) to this harness which must be attached to a ground bolt. This wire is not inside the jacket like the others so I just snaked the extra ground wire thru the laced cover and attached it to a ground bolt by the tow plug at the kick panel. There all approx the same length and it just looks nicer with all the wires covered by the jacket."
And, if all else fails, read the instructions:
Tekonsha