I think Diver300 has a good idea, but maybe a car wiper motor might be overkill in terms of power, depending on the size and weight of your display. A surplus gearmotor might be ample, and if you shop around you can more than likely find one that is geared appropriately for your application in terms of weight and speed requirements.
Without using a microcontroller, I think the simplest way is, again, as Diver300 suggests. Rig trigger contacts on the ,moving part of the display for its fully open and fully closed positions. Have a circuit connecting the triggers to a 555 timer, which can be wired (with a potentiometer, if you wish to have control over adjusting the delay times) to delay the closing of the display once it's opened.