In my opinion, if the original design was to have a fan at the top of the shaft then it will be required to provide the correct amount of extract. So I would suggest that it requires maintenance. As for operating the motor, I take it there is a control unit for the fan somewhere. It could either be operated by a fireman’s key switch or the manual doors may have switches fitted to operate the fan when door is opened.
I know it was a slightly more modern building (2004) but what was fitted there was a smoke shaft with doors on each level, but each door had a door opening unit which was held closed using a magnetic lock connected to the fire system. In the event of a fire on the floor, the door would open smoke would be extracted by a vacuum caused by outside air passing over the top of the shaft.
Where about are the premises? PM me.