I have no parkiing lights on my car when the headlights are on.

I have a multimeter and test lights available for my use. I also own a Snapon 2500 scanner with OBD1 hookups. Please answer my question as quickly as possible,

Does the radio display dim when you turn on the head lights? If it does, the head light switch is working and there's a break in the wiring after that. If not, we need to test right at the switch. In particular, check the connector body for signs of melting and blackened terminals.

The radio display does dim when the headlights are on. Should i check the wiring at the taillights themselves to see if there is any shorts there.

I assumed all of the parking lights were not working. You didn't say whether just the back ones were out or all four corners. If the front ones work, it's pretty obvious the headlight switch is working. In that case, yes, look at the wiring in the trunk. You would not be looking for a short because that would cause a fuse to blow and none of the lights would work. Look for an open circuit. We used to find a lot of corroded wires where people used ScotchLok connectors to splice in a trailer wiring harness. Those do not seal out moisture. Also check electrical connectors for corroded terminals. As I recall, there is a connector behind the left kick panel to the left of the driver's foot area.

I checked fuse number 5 and I found that it had power going to it> I will check the headlight switch and the wiring going to it.

dodgeram150, were you able to fix this problem? Do you need a wiring schematic for the exterior lights?