You can configure the taskbars to behave differently and only show the programs running in that monitor. I wouldn't talk about it if I wasn't 100% sure it is possible. I'm used to working with two (or even 3) monitors. And AutoHotkey can be in the hidden section of the taskbar icons and still run fine.
Requiring to show the mouse is not an optimal solution because not everybody has a cam, and even if you have a cam, it may be impossible to change its angle and still play (like on a laptop, for example). But having a clicker counter on screen shouldn't be hard to enforce.
I think the click counter and/or the cam as proof of no auto clicker are fine. But showing your taskbar doesn't prove anything. A lot of people have two monitors and, thus, two taskbars. You can easily run the auto clicker on the other monitor and not having it show on the video. And even with a single monitor, AutoHotkey scripts don't have to show on the taskbar to run.
I don't know if this is relevant or if it's already on discussion. But I haven't seen anybody else comment on it, so there go my thoughts.
I know there is a very recent question about emulators. But when it is true that one of the mods recommended Mesen, there are other games with lists of authorised emulators that don't include Mesen. Since the rules for this game don't include a list if authorised emulators I prefer to be sure before deciding which emulator to use. And Mesen seems to be the best NES Emu right now.