Do your guys' parking light fuses blow any time power is applied to them? Or does the fuse stay intact when you apply power?
My sons truck blows the fuse every time the switch is turned on. That tells me that there is a dead short somewhere. We started by disconnecting the bulbs and isolating each of the 10 or so lights that come on with the parking light switch. The eight I counted were the two front parking lights, front fender parking lights, bedside parking lights, tail lights and two license plate illumination lights.
We didn't get anywhere with that check, so we are about to start trying to pull apart the tail/parking light wires and trace them along frame, into distribution block, into cab, etc. Has to be grounding somewhere, to blow the fuse. Suppose it could be in the headlight switch, too.
If it's not blowing the fuse, I'd be suspect of the switch, or power supply coming into the switch.
Nik