Headlights do not work when transmission is in park

That is actually working as designed if that car has the twilight sentinel and DRL option for the headlights. The DRLs also only operate with the key on and in gear only and should switch to the normal headlamp mode once it is dark. That should be fully automatic based on the input signal from the light sensor on the dash. That car should also have the twilight sentinel option, with it the headlights will stay on for an adjustable amount of time if you pull up and shut off the engine and it is dark enough that the headlights were on. The headlight switch can override the automatic switching, but it still needs the park signal to turn the lights on. There is a way to modify it so the switch controls it all but then you lose the DRL controls.

It can be a bit strange when you are not used to it. It's even more fun because it was an option so the first one you drive may have it, the next one doesn't and then you start to wonder if something is wrong. Personally I'd rather have a nice simple switch, much fewer parts to go bad in the future. Some modules in those vehicles are already on the NLA list because they were not big sellers.
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