Lets troubleshoot random electrical issue with 2012 Sonata

My brother has owned a 2012 Hyundai Sonata for several years. He had to jump a relatively new battery a couple of weeks ago to resolve a no-start condition, but it had been working fine since then. Today he says that the headlight switch has essentially inverted itself and that the headlights only come on when the switch is in the "off" position. Taillights, brake lights, turn signals, and high beam headlights all function normally.

Any ideas what might be going on here? I'm not able to put hands on the car to check/test things but it piqued my curiosity and I thought I'd get some insight from the best and brightest corner of the automotive internet.

Is it possible that you're getting DRLs out of the headlights in the "Off" position and interpreting that as headlights on?

Without wiring diagram, it's pretty tough to troubleshoot. That taillights are working as expected would have me guessing at a relay rather than the switch. 

I asked about DRLs, and was told that it's the headlights for sure. But who knows. A relay failure could make sense of the sudden onset...