When you plug the driver's seatbelt in, it closes a circuit that turns off the out of park alarm. You can either disable it permanently by shorting the two wires together or you can put a switch somewhere in the wire that you are using to short.
Your service manual is available online here:
http://hemitruckclub.com/04manual/19078-dr_intlpdf.pdf
You can read about the switch on page 80-51 (pg 670 of the PDF).
The relevant wiring diagram is shown on page 8W-40-2 (pg 937 of the PDF).
For non-SLT's, the relevant connector is C311 shown on page 8W-80-38 (page 1087 of the PDF).
For SLT's, the relevant connector is C322 shown on page 8W-80-41 (page 1090 of the PDF).
For both the SLT and the non-SLT, you are looking to short the skinny 20 gauge Violet wire with light green stripe to the skinny black wire (there's also a fat black wire).
For '06's, it's even easier, since it is only a two wire connector. You just unplug the seat belt buckle and use a female spade connector as a jumper on the body side connector.
For other years, it's the same concept, just download the appropriate service manual from hemitruckclub.com and check the instrument cluster section of the wiring diagram.