I have narrowed my problem of no working lights on
No, I wouldn't suspect the headlight switch. Something more sinister, more surreal, too: a module, maybe a body control module, or a light control module, probably under the dash somewhere. GM began using a lighting control module (LCM) at least as far back as 1992, tucked unhandily up under the dash, and wired between the headlight switch and everything else in the lighting circuits. Normal to suspect the headlight switch, but the odd conjunction of the car running and the headlights' actions suggest a module (another computer!) may be in there. The headlight switch should have no effect on it if the engine was running or not. You would have to see a wiring diagram in a repair manual to check. I am not familiar with your Hyundai, but if you could find a diagram, you should be able to fix it. If you register for free at autozone.com, giving make, model, year and engine size of vehicle, you can access wiring diagrams and repair procedures. Just look under repair guides.Wiring diagrams were under Chassis Electrical, if I recall.