Unfortunately, the owner's manual leaves out a step...
Turn down visor, so that it is perpendicular to the roof (not flat against the roof) (covering the top portion of the front windshield). Do not rotate it to the sides of the car (covering the top portion of the side door windows)
Slide open door for vanity mirror.
Turn vanity mirror light switch on.
NOW will your vanity mirror lights work.
(Usual problem for not turning the lights on when you'd expect:
* forgot to turn light swtich into on position
* forgot to open the vanity mirror
* turned the visor to the door position )