The low oil sensor for the VMM is actually more than just a low level sensor. It is also a temperature sensor. I think that basically, it looks like the ECT sensor, except that the electrical circuit is not continuous. Oil needs to be present at the gap in the sensor to complete the circuit and allow a temperature reading to take place. Obviously, if the circuit is open, then the "LOW OIL" light comes on.
If your sensor does not trip when the oil level is low, then I would suggest that you remove it during the next oil change and give it a good cleaning. There is probably some sort of sludge or debris keeping the circuit continuously closed.
I believe that, if the circuit was perpetually open, because the harness plug or wiring was loose, that the "LOW OIL" light would be on all the time. And if the wiring was shorted, then the light would never come on.
If the "CHANGE OIL" light comes on every 1000 miles or so, that means that the temperature-sensing portion of the sensor is not working. The VMM therefore is telling you to change the oil on the most severe service schedule there is, based on bad data from the sensor.
I don't know why the temperature-sensing portion of the sensor can fail sometimes. I have had 2 Thunderbirds in which it worked perfectly for years, and 1 in which it didn't work from the time I got the car. It just works ... unless it doesn't.