Just now I played with the headlight switch. Turned auto light control on. No green indicator on dash. Headlights are on...low beam. High beams do not click on.
This is correct for daylight operation mode. DRLs are on; "headlight mode" with taillights/dash lights dimmed is off.
Turn headlight switch all the way to right. Green indicator light on dash is on. Headlights are on...low beam. Able to click high beams on. Lights are still on when car is turned off.
Again, this is correct for this mode. Your high beam stalk and high beams are working properly.
So, left to its own devices in the regular "Auto" mode on the light switch, the car should turn on the auto light "headlight mode" when it gets dark outside, which will dim the dash lights, turn on the taillights, and enable you to switch to high beams with the stalk. If it is NOT doing this, the little dome sensor at the base of the windshield may be bad.