I do not believe the new switch you just bought is going to serve your needs. It looks like it's made for an older truck that did not originally have turnsignals and dual filament bulbs. I don't like the "stop" lever shown on the side of the unit you bought.
What I would do is go to the auto parts store and buy a trailer tow light box adapter for about $12, and then use a simple on-off-on single pole toggle switch. Mounting the toggle switch will be the hardest part.
The trick to turnsignal switches are their ability to let the stop light function through, as well as the turnsignal function, for the rear lights. The box I am talking about achieves this. The box is really made to take European vehicles and others like Ford explorers that have the separate amber turnsignal bulbs, and combine the red brake lights and the amber turnsignals together so they will operate a trailer that has the American style red only turn/stop combo bulbs.
I used this on my 53 Ford f100, and it works well.
Your wires on your truck are;
left front turn=green/white
right front turn=white/blue
left rear turn/stop=yellow
right rear turn/stop=green
input from flasher=blue
input from stopswitch=red/black