One more thing to note:
Blinkers are "blinked" by a thermal switch. Lets say you have 2 blinker lights at 25watts a piece. When you turn on your turn indicator, the current (50 watts) passes through this thermal switch, which heats it up. Once it reaches a certain temperature, there's a metal bar that expands and disconnects the circuit. Once it cools off, it falls back and re-energizes the circuit. And repeat.
The problem, when you add the a trailer (at 25 watts) onto that circuit you increase the current to 75 watts. The metal bar heats up in half the time. The result is that you'll get a rapid blinking light.
Usually, with the purchase of a towing package, the manufacture adds a relay or a heavy duty flasher to take care of this. On some of the manufactures, the relay is already installed, once you plug the harness in it activates the relay.
The good news, if you have fast blinker problem you can swap out your flasher switch/relay for about $12-15. Hit the autoparts store, it'd be in the section with automotive light bulbs. "Heavy Duty Electronic Flasher." The flasher goes into the fuse panel on your truck.
This is how things used to be up through the 90s. I suspect it's still the same way, though I'm not 100% sure how the manufactures handle 'flashing' now. Perhaps this will be a non-issue for you. If you do splice wires, I'd recommend just trying it, then solving the fast blinking problem later, should it arise.
Here's an example of one. I couldn't find one for a 05 Sequioa so I punched in chevy pickup.
http://www.partsamerica.com/ProductDetail.aspx?mfrcode=TRD&mfrpartnumber=LF12& parttype=121&ptset=A