Hyundai Elantra 2007 Recommendations?

I/m having a issue with my car, not totally serious by any means more of a annoyance. when my a/c or heat is on everythings fine but when I turn everything off I hear a click and that little green light on the a/c knob turns on and off. would anyone know what would be the cause of this and a options on how to fix it?

Secondly I'm gonna be doing a tune-up on my car wanted to see what would be the recommendations on plugs and wires?