What "do something mysterious" does in EarthBound
0I read that, somewhere on starmen.net's forums, that all the "do something very mysterious" battle action in EarthBound does is call the code for Brainshock, the confusion spell. I think Nitrodon was the one who figured this out, so credits to him.
The problem is, this action is only ever used on you by enemies, and it almost never works thanks to the way the game calculates Brainshock resistance. Here, what I've done is hack King to spam this move on a target that is susceptible to Brainshock.
I filmed this video 15 or so years ago, hence the potato quality. I used ZSNES because I still like it. (ZMZ rules!)
A bit more of a technical explanation of Brainshock resistance:
Every entity in EarthBound's combat system has a Hypnosis resistance. However, an enemy's Brainshock resistance is not stored separately. Rather, it's derived from the Hypnosis resistance, being effectively the opposite. In other words, if you resist Hypnosis, you'll be weak to Brainshock and vice versa.
By default, the Chosen Four are more or less immune to Brainshock, but very weak to Hypnosis. The only way to change this is by equipping particular arm equipment, but there aren't that many items that even allow you to change this value to begin with. You're not going to have access to any of the items that do this by the time you encounter the enemies that can even do the "do something very mysterious" action, so they become a wasted turn. However, if your team somehow has Hypnosis resistance, you become vulnerable to it. Using this, I try the move on a Spiteful Crow, which Brainshock has a 10% success rate on, and it eventually works.
As for where I got this data, this page might help:
https://starmen.net/mother2/gameinfo/technical/equations.php
Partway down the page is where you can see the technical details of how Hypnosis and Brainshock work, and they do a hell of a lot better of a job describing this than I am right now.