You can't tap into the tail light, that will make the 3rd brake light blink when you make a turn and move the signal lever.
I don't think you will find the proper connection that the trailer connector either. The only one that may work is the wire for the electric brakes, and that's not going to work unless you have a brake controller, and it will also not be completely bright, depending on how strong you have the brakes set up.
I have heard rumors there is a box you can buy, that will take the signals from the taillights, and convert it to 3rd brakelight use. The box keeps it from blinking when you use the turnsignal. I don't know where you can buy this box though, you might do a web search and see if it's really available.
The only other solution would be to tap into the 3rd brake light wire that is in the rear of the cab. It's just a single wire that comes directly from the brake switch on the brake pedal.
The rear brake lights and turn lights on American cars and trucks(most but not all) use the same bulb for the brake and the turnsignal. Only the cars with the rear amber turnsignals use a separate bulb for the brake lights.