"However, when my fuel gauge "drops" to empty, the low fuel warning light does not come on. Does yours? With the needle on empty, shouldn't the low fuel light come on even if the information from the sensors is wrong?"
If your sensor is similar in design to that in our 190E - no. The low fuel sensor is a closure switch on the float mechanism, and is triggered when the float hits bottom. The loss of fuel level reading corresponds to a sensor resistance of 'infinite Ohms' when poor contact occurs at the float wiper. Since 'empty' on the gauge is the highest resistance of the sensor, that is he end of the gauge the needle goes to when the sensor loses contact. The float is still where it should be.
'91 MB 190E 2.3
'08 RAV4 Ltd 3.5
'83 Lazy Daze m'home 5.7