Bushwacker, I feel VERY confident that you have a bad sender in the Motor Mounted oil tank. These are notorious for going bad and can be diagnosed within minutes. The sender in the tank is no different than what is in a fuel tank. When the sensor drops in relation to the level of the oil going down, it beeps indicating to the operator that you only have "X" amount of oil remaining and to fill it up ASAP. The sensor, when bad will give a false reading. Your tank can be 100% filled and air free but do to a faulty sensor, still give the warning beeps you are indicating.
I will post pictures tonight of how you can determine that the oil tank is faulty using the jumper wire. I would do it now but my wife has our digital camera with her.