One of my Drakes has the "air vent" in the tank; the other doesn't, even though I bought them at the same time. (Drake original rather than Drake II.) That cutaway may indeed be an air vent that helps the flush, but it also seems to have been added as a feature at about the same time as Toto introduced the Washlet with the automatic flush device. The wires for the automatic flush device are to be routed through that cutaway, so at a minimum it has been added for that purpose. I don't think you are harming anything by covering it. Duct tape is vapor-proof, generally-speaking. If you want something more waterproof, you could try "rescue tape", which is clear, but the duct tape should be fine.
I would call Toto customer service. 1-800-295-8134. I would complain about the damage to my wallpaper from the cutaway, and I would ask them, "Why does this thing have this cutaway, anyway? It has damaged my wallpaper, and I am disinclined to buy the three more than I planned to buy because of this." They are very nice folks in Georgia and they may have a solution for you. Moreover, I think that Toto should hear your feedback, and, being a Japanese-owned American company, they most assuredly keep scrupulous track of customer feedback. I truly think that this cutaway was added primarily to facilitate the auto-flush washlet, and to make it convenient to install that washlet. If you don't want that washlet, I think Toto should provide an option that doesn't cause water vapor to stain your wall; either a different tank lid (or tank in my case) or a device to cover the hole.
Because my Drake stands off the wall 1.125", staining isn't an issue for me, but I strongly suspect that this is an unintended (and unimagined) consequence of the design change.