My parking light will not turn on when my headlight switch is on?

Everything you described points to the head light switch itself, especially when the lights do work when the switch is held in a certain position. That proves all the rest of the wiring and fuses have to be okay. The only exception would be if the running light circuit has a switch contact that is just barely sliding over a different 12-volt supply contact for a different circuit, but that would be really unlikely.

What we need to do is pull the switch out, then start by looking at the electrical connector to see if two terminals are black / overheated, and if the plastic connector body is melted around those terminals. If they are, the only proper repair is to replace the switch and those two terminals in the connector at the same time. If either the switch or the two terminals are not replaced, they will cause a repeat failure of the new part.

Here's the diagram. The running lights are on the first and third diagrams where I added the colored arrows. Next are the switch removal instructions, but it sounds like you may have had that out already. The last photo is of the switch terminals. I can't find terminal "R", but the red arrow is pointing to the supply terminal, "B2". That one will have a pink / red wire. The wire going to the lights is black / yellow. That circuit also feeds the dash lights. They both feed the radio display, so you'll see it doesn't dim when the head lights are turned on.

Those are the two color wires to look at for overheated terminals.

Typically by the time the lights get this bad you're going to find the terminals on the switch are black, the switch body itself is charred around their rivets, and the plastic connector body around those two terminals is melted. If that is what you find, cut those two terminals out and cut away the melted plastic around them. Plug what's left into the new switch.

The two overheated wires will be hardened from being hot and solder won't adhere to that. Cut away four or five inches of those wires, then splice in the same amount of the same gauge wire. Seal those splices with heat-shrink tubing. Don't use electrical tape in the truck as it will unravel into a gooey mess on a hot day.

At this point, if you choose, you can harvest a pair or replacement terminals from a salvage yard along with the sections of wire still attached. I prefer to use a pair of crimp-style universal spade terminals, but also solder those crimped connections for best connection. Now those two wires can be plugged onto the switch individually. I like to squeeze them first with a needle nose pliers so they make really solid contact.
If you accidentally switch them when you plug them in, no damage will occur, but the dash lights will be powered up all the time and drain the battery.

Let me know if that's what you find or if we need to go in a different direction.

Hi,

It sounds like the switch needs to be replaced. As far as the power you mentioned, power to the headlamp switch is provided by two different fuses that have power at all times, fuse 2 in the power distribution center and fuse 14 in the interior fuse box.

The parking lamps are powered via fuse 14. Have you checked it?

Let me know. Also, pic 1 below is from the headlamp wiring schematic. Pics 2 and 3 are from the exterior lamps. I had to cut the single page in two so you can read it. I did overlap the two. Note fuse 14 is present in both schematics.

Let me know if this helps or if you have questions.

Take care,

Joe

See pics below.

Hi,

Thanks for the update. I'm glad to know you found the issue.

Feel free to come back anytime in the future. You are always welcome.

Take care,

Joe

Happy too to hear you found it. Remember, this is absolutely going to occur again unless you replace the switch at the same time.

"Happy Thursday to you all both".