My front parking / marker lights go out when my headlights are switched on. “Why?”, is a common question. You may expect both should be on at the same time. Apparently it was a thing in the 60s, at least for GM, to have the headlight switch work this way on several models.
If you want your front parking / marker lights to remain on when the switch is pulled to headlights, there are many forum threads and posts about this. Some suggest adding a jumper wire to the headlight switch from Light Blue (headlights) to the Purple (front parking lights). While this may allow the parking / marker light to remain on during headlight operation, it will also cause the headlights to be on in the parking / marker light switch position. meaning you will not have parking / marker light only operation.
If you want to keep front parking / marker lights only operation and also have the parking / marker lights illuminate during headlight operation, I suggest a safer and neater way is to wire in a simple relay as shown in the image below.