It seems to me that the position of the head would have a great deal to with it, as would the general, uh, bugginess of the eyes. Which brings up another reason for closing/covering the eyes and/or putting a sheet over the corpse: keeping away flies.
Of course I’m just speculating here, and with any luck it will remain speculative for some time.
That site is a scholarly review of the question of whether it was Jewish custom to put coins on the eyes of the dead in the 1st century. They agree that it was not. It was, however a Greek custom.
The writer goes on to say that the coins were more often placed in the mouths of the dead as a Jewish custom.
I don’t agree that the page as a whole settles the question of whether other, later, cultures placed coins as a symbolic rite or for the mundane purpose of holding down eyes.
If it’s happening right outside the window, it is as near simultaneous as dammit.
I don’t always draw the eyes of dead characters for my TV show, but when I do, I prefer dos equis.