Electricity half broken in my 1996 Buick Century?

This will sound absurd but I swear to GOD I am speaking about my real experience with my car.

Sometimes (like 75% of the time) when I put my car (1996 Buick Century) into park, the locks won't engage. That's fine, whatever. The problem arises when whatever is powering my locks also connects to my headlights (and my dash/interior lights but that matters less). My blinkers work completely fine even when my headlights don't and have been my only source of light while driving. Sometimes it will just spark back to life as I'm driving, too! The locks and lights turn on, and I've only had them turn off, momentarily, while driving once.

My dad is a well-versed hobby mechanic and has previously fixed my car, he's checked "everything short of ripping out the dash" to find whatever is causing it and STILL nothing. It's not a fuse or, seemingly, no wires or other connections either.

I work the night shift at my job and I need working headlights, but my car is also my prized possession and I really want to fix her. It's been incredibly hot and humid in my area, could that be the problem? Has anyone experienced this? Is there a way to fix it? Preferably quickly.