Looking at this video now, I can see the strategy I've used is a bit extraneous. All you need to do is put the eyeball near the entry hole so that it gets rolled to the right. Place the little bar vertically on the ground so the eyeball bounces off it, through the gap and onto the red button.
Yashar Kamyar also sent in these two other solutions:
Christoph Kment gave us this way of hitting the switch:
Wassim Bejaoui has this alternative suggestion: