Before you take off the alternator. If it is like the one in my 91 300e you can remove the regulator and brushes with the alternator in place. When my alternator failed the abs and srs light came on then the car died shortly thereafter. The battery light never came on. The brushes wore down to the point where they were no longer making contact and the alternator stops charging. When battery voltage drops to about 10 or so volts the abs and airbag circuits light up because of low voltage. I think the brushes are part of the circuit to light the battery light and since they are no longer making contact the light won't light up.