Whilst this maybe a good idea for staff woring within the home to use their time wisely in an emergency, I suggest you contact your local fire service before spending money on the signs, to enquire whether they have any value for fire crews attending.
There are many issues to consider including:
A simple sliding sign may be 'operated' by moving traffic in the corridor (especially clumsy firefighters moving in breathing aparatus).
How certain are you that residents will comply or remember to 'book in'? (to be effective any booking in system has to be at least 100% reliable)
In virtually all fire situations, firefighters will be tasked with searching all rooms and would, in my experience, not regard such door signs as an indication that the room is clear - that is if they could see them in perhaps limited visibility.
I'd run this idea past the people who would have to use it. Contact the operational fire crews (as they would be expected to se the system) as well as fire safety officers to get the best advice