Pizzaguy,
I've been meaning to report back in on this matter. I conducted the suggested experiment you proposed and just keep forgetting to report back.
Interestingly, when you use the switch on the console to raise and lock the spoiler, it does NOT beep when it reaches the top, fully extended position. When you lower it back into the fully seated position using the switch then it DOES beep. And driving around with it locked up did nothing to change the problem of the light remaining illuminated at all times.
So far, so good with the new battery.