Thinking about it and looking closer, is there a sticky pad behind the round button? 🤔
If you're brave enough to investigate might it just be one of those cheapo 'fake alarm' buttons... literally a button battery and LED. I've seen similar advertised, gives the appearance of an aftermarket alarm without the cost. If the battery has run out it would also explain why it doesn't do anything.
Just a suggestion (I take no responsibility for the consequences 🤣) but give it a gentle wiggle. If its properly affixed THROUGH the centre console you should be able to feel it, but if its literally just stuck ON the console it'll probably not take much wiggling.