Then it should light up when the request is acknowledged, and stay lit up until the elevator arrives.
But wait, there's more: when the elevator arrives until it leaves, the button should flash or change to a more prominent color. Why? Because imagine someone presses up and someone else presses down, and the elevator arrives going up. If the up button switches off at this point, now only the down button is lit which clearly signals the elevator is going down, which is wrong.
But then you might tap the button and think it's broken, because it does nothing. The light means "this button works", not "your desired action has registered".
I guess you might want to fade it from red to green (red being "this works" and green being "it'll do what I want"), but I don't mind the holding-down behaviour. The only problem is that you can never know how long you need to hold it down for unless you stop holding it.
Perhaps we’re not talking about the same thing. What I refer to has the button light up while you bump it, and then go dark again, whereas if you press it more deliberately, it stays lit (and takes effect). This can apply to the buttons inside or outside the lift.