You are correct that the parking lights are only on with the head lights off.
It may stem from old laws about driving with parking lights on. I recall a news article some years back when we first moved to Nebraska. In the article, Omaha police were ticketing drivers whose new vehicles had the parking lights on with the headlights on. It was such a big thing, that it ended up in court. As I recall, the defendant's case won based on the fact that newer cars were built with the feature of the parking lights and head lights on together as a safety feature.
I haven't looked in a wiring diagram to see for certain the best way to accomplish the modification. What I do see is that power for the park lamp circuit and the head light circuit has to remain the same at the switch in order to have each function as they were originally designed.
By simply combining the two circuits, control is lost to run park lamps independently if the power for both circuits comes only from the park lamp terminal at the switch or the headlight terminal at the switch.
Now to make the park lamp circuit function with the headlights on also, it requires the headlight circuit to power the parking lamps also when the light switch is pulled out to the second stop of the switch.
What I see, even through my current chemo induced foggy brain, is the connections at the switch must remain as they are but with a modification done downstream using a diode to control the flow of power. For those reading this that do not understand electrical well, a diode is like a gate. it allows electricity to flow in one direction but not in the other.
So, placing a diode in the headlight circuit to open the gate when the switch is pulled out to the second stop, original headlight only position, allows power to feed both headlights and park lamps. If the switch is pulled out to the first stop, the park lamps only work because the diode will not allow power to flow through the gate to the headlights. Hope that is somewhat clear.
I sketched a diagram of this but need to clean it up a little before posting. It should be bench tested to insure it actually works as desired.
Loren