Headlight plug pinout needed?

It looks like they share a common ground in the black wires from the wiring diagram. A quick test would be to run a wire to battery negative and then use a needle to probe the black wire in the lamp connector and touch the battery ground to it. If the light works you can go hunt the bad ground. Kia does what others do and stack the grounds so you can end up with 5 items grounded to one place and only have one of them corrode so they don't ground.

Sadly, that is the only headlamp connector they show for the K5 in any version. Kia can be bad that way, they put up a one size fit's most diagram for connectors. However, the wiring diagram should be correct. Don't trust that the ground looks good, it's common for them to look perfect but still not be a good ground. That is why I suggest testing them at the lamp end. The other thing that you could try would be to plug the light into the other side and see if it works there. That would at least narrow it down to being the wiring in the car and not a bad unit. You can also test the grounds using a test light, connect the test light to a known good power and see if it lights on all the black wires. Then connect it to a good ground and see if it lights up with the parking and turn lights on.

Okay, you have only the right front turn and parking LEDs out, correct? Left side and rears all work? DRLs work? Asking because from what I can see on the wiring diagrams the only item they share is the ground connection. Power feeds are different, control circuits are different as well. What do the turn lamps do if you turn on the hazard lights? You say the front is apart from an accident or? Wondering if maybe the harness got pinched and cut the power feed wires to those lights.

OK time to go back to basics. Take a test light and connect it to a known ground. Turn on the turn signal for that side. Now gently probe the pins in the connector. Do you find one where the light flashes? Turn it off. Turn on the marker lights and do the same. Trying to discover if the issue is in the vehicle or the light. In reading through everything again I'm wondering if the IPS might have been damaged by the first light you tried as it worked. It uses individual driver transistors for each light and it's a possible failure point. Do you have a scan tool that can talk to the various modules? That one can be controlled and tested using a scan tool. That would let you see if there are any error codes in it as well. The last test would be to use the test light right at the ECU. Look for the middle connector on the module under the dash. The lighting feeds come out of that ICU B connector. Pin 5 should be a Blue wire that feeds the turn signal, with the signal on that pin should flash a test light.
Pin 14 should be a White wire, it should light a test light with the marker lamps on. If those work at the module but not at the light then the wiring is the issue. If they don't work at the connector on the module then the module failed. The book shows it as a simple remove and replace. Disconnect the battery, then remove the connectors, unbolt the module, remove the rear connectors and reverse that to install the replacement.

Okay, in that case it sounds like you got a bad part. Did you try the PS in the DS? At least if the DS worked in the other side, it narrows it down. Unless they changed something wiring wise in the lamp assemblies. Are the lights you have from the same year or are they "compatible" parts? Service info doesn't point at any changes but Kia is somewhat spotty with info at times.