My 2003 Durango shuts off when you put it in park. The auto place says it's my neutral switch. Do you agree? Also, if so, where is the neutral switch?

The neutral safety switch on my 2003 durango is inside the transmission on top of the valve body. Some of them have one which can be removed from the outside.

The purpose of the neutral safety switch is to allow the starting (cranking) of the car in only park and neutral. It also doubles as a reverse light switch.

I don't think the ignition power travels through the safety switch, also called the Range Sensor.