RE 'a sort of void created by the rear window'

That void is a low pressure zone designed to pull hot air up through the bay when moving, its a deliberate bit of aerodynamic design for cooling, not just to look good (to some).

It also creates another problem as you dont really want too much low pressure zone above your rear wheels at great speed, so the bigger or higher a rear wing is sticking up into the air stream (or out to the sides), then the better.

But only so much big or hi wing is a good idea, you can start getting the front to lift with too much pressing down at the back, so have to add something more at the front end, then you get into adding too much drag and need more power to pull it along!

Its a balancing act.

But a fan would only aid cooling in this case mate, especialy when in traffic jams...
unless you go along the lines of the infamous Brabham fan car, which would be all kinds of cooool.