Need help automatically closing shutter doors

Hi all,

I have a bit of a problem that I would like to solve the smart way;
We have a workshop with a shutter door that opens up to our showroom,
and unfortunately the people who close up often forget to close these doors.
The result is my motion sensors going off all through the night,
everytime a car passes by and shines their headlights in through the open door.

So then…
I don’t want any rigid actuators that render human control impossible,
nor do I want to springload the doors to always automatically close.
Are there devices that can push a door shut, but only once, at a given time?

Ive been thinking about using an arduino or similar, to turn a servo with a stiff spring on it,
but then both sides would always have a long rod just jutting out, and im not sure I like that.

For illustrative purposes, heres a picture of a similar door;

Does anyone have any interesting ideas?