Driver’s side running light not working?

Okay, there are fuses for the front marker and park lights. A quick fuse test is to turn on the parking lights, do all the front marker lamps come on? If both are off, look at the fuse in the junction box near the battery. If one is out but not it isn't the fuse, instead it is in the wiring. The brown wire is the power feed, and the black is ground. Now for the corner light it works a bit differently. It has the brown feed, but the blue wire is a feed from the turn signal. When the turn signal is off the bulb will light up with the parking light, when the turn signal turns on the 12-volt feed to both sides of the bulb instead turn the bulb off. That makes it flash opposite the front turn signal. Then if the lights are off and you use the turn signal the power goes to both the front turn bulb and the corner lamp. The corner lamp now finds a ground through the front marker bulb, so it flashes with the turn signal.
You say it is the front marker only? Does the corner lamp work both as marker and turn? If yes, then it's easier to trace the problem. Attached is the wiring, a very quick test would be to use a pin and test light. Push the pin into the brown wire outside the connector at the housing, now turn on the marker lights and use a test light connected to ground and see if there is power there. If there is, the problem is corrosion in the connector, get a pigtail and replace it. If there is no power there are two options, trace the wire up and under the fuse box and see if it's corroded there (very common on those trucks) or if it failed farther along. Replace the bad wire. Or if you want to test it and even repair it simpler, just run a bypass line from the brown wire on the passenger side over to the brown wire on the driver's side. That would get it to work at least.

Okay, wires crossed you mean the Daytime running lamps. Those are even simpler. There is a DRL relay that feeds both lights, Power in on the dark purple and black is the ground. If one side works but not the other everything to the relay is good and it's a wiring problem in the power or ground to the out light. Test the wire where it gets to the socket as above. No power there means the fault is farther up. To save aggravation you could simply bridge the purple wires at each lamp with a jumper wire but again, they like to fail at the crimp inside the sockets.

Was it a bad socket or broken wire?

Thanks for the feedback, I sort of expected that was where it would be. Seems to be a common issue with that vintage.