Not knowing what flavour of engine it is (2/ 4 / etc stroke) The high level observation I would thorw in here is that on older machines the alarm was usually trigered by a switch (e.g bimetallic strip type thing on the temp, on / off on the oil float) and so for it to be squealing (if it is an older 2- stroke) I'd be guessing a short or an uncalibrated sensor. Modern ones controlled by the engine management I'll leave to the experts!
You say you keep the oil level low - does topping it up help? I have had a couple of car fuel gauges in the past which had a sticky float mechanism, and didn't register I had filled it until the first pothole / speed bump loosened the float. Is your oil level float sliding properly, or is it stuck at "warn" and doesn't move when you drop the engine? If the float is towards the rear of the tank it will register "low" as you tilt & the oil moves forward.....