My understanding has always been that, at least in the US, it is usually the case that the "close door" button doesn't do anything unless there is a firefighter

My understanding has always been that, at least in the US, it is usually the case that the "close door" button doesn't do anything unless there is a firefighter key inserted and the elevator in fire mode. That's really there to allow a firefighter to manually control the door open/close functions during fire-ground operations where you really don't want the elevator doing things on its own. There are, of course, always exceptions. Some reading I did earlier suggests that there is some variation based on elevator brand, and possibly even then whims of the building owner (in terms of what instructions they gave the elevator installer about how they wanted things to work). Curiously though the "door open" button does usually pre-empt the (automatic) closing of the door, even in "normal" mode. At least IME.