DING (me chiming in

)
That is the connector to the oil level sensor. According to my manual, the sensor is a simple float that connects the signal to ground through a switch, when the oil level is OK.
Here is what the connector pins should be:
Pin A - Brown Wire - Engine Oil Level Indicator Input (to PCM)
Pin B - Black/White - Ground
So I would "guess" that either the sensor is going bad, or there is a connection problem between the sensor and the wiring going back to the PCM.
I would use a multi-meter and make sure the sensor is working (should ready zero ohms between the sensor pins). If that is OK, it is a wiring issue.
One other note: My manual says that the condition has to exist for at least 20 seconds before the light will come on.
Hope this helps.
Take Care,