It does depend on what kind of mirror you got. '93-early production '96 Explorers...XLT, Eddie Bauer, or Limiteds, have more of a rectangular shaped mirror with buttons (Auto Mirror, Dim, and Autolamp On-Off switches, and a slider for headlight off delay) along the bottom of the mirror. While the late '96-'01 (4-door) or late '96-03 (Sport/Sport Trac) have more of an oval shaped mirror with only a slider at the bottom. That version of mirror has no on-off switches for dimming nor headlamp delay.
To your question, if I read it correctly, you have the 1st gen mirror, which is the rectangular shaped mirror with 3 buttons and a slider switch. If so, then your auto dimming function will only work IF you turn it on. So you have the press the button on the left in order to turn it on. Once you press the button, the green LED will be lit, telling you that the mirror is functioning. You can test it out by placing something dark such as your hand at the front of the mirror sensor (facing the windshield) and shine a light at the sensor that is on the mirror (facing the rear). If the "Dim" button lights up, then you will see the mirror progressively dims itself. If it doesn't light up, it's either the mirror is broken, or it's not dark enough for it to function. Note: The mirror will only function when the sensor at the front of the mirror senses darkness. The mirror will not work in daylight, eventhough the auto dimming function is switched on.
The "Dim" button will temporarily dims your mirror to the maximum degree. It usually last about a minute. This function will work at anytime, whether the mirror was switched on or not.
The "Autolamp" button will let the sensor at the base of the mirror (at the windshield) to sense darkness. If it senses darkness, then the headlamps, parking lamps, and your interior dash lightings will be switched on, just like you were turning the headlights on yourself. The slider is the delay for headlights. The headlights can be switched off as soon as 3 seconds to as long as 3 minutes.
If you're in daylight and get into garages or stuck under a bridge, your headlights will not be automatically turned on until you're under there for at least 30 seconds. This will prevent any shorts in the wirings or decreasing the life of the bulbs.
I hope this explaination is clear. If it doesn't make sense, please reply. I'm very very sleepy...3 hours of sleep last night from studying may not help me type as well today.