This one's pretty simple: avoid writing about them as much as you can. I'm going to add more stuff, but it all basically boils down to this.

Mysterious Wizards can not be the (or a) main character. If they are, you'll have to explore them more and then they won't be Mysterious.

What a Mysterious Wizard can be is:
•Crazy Person
•Bad Guy
•Gandalf
•Dragon

Before we go further, I must stress that these are categories. None of these characters are always Mysterious Wizards. Spike, Ember, and Ember's dad, for example, are not.

Also, a Mysterious Wizard can lose their position at any time. If they stop being a Mysterious Wizard, it's usually permanent, though for some characters their status can constantly change. It's usually the Crazy People that can ascend back to Mysterious Wizard after losing the title. Like Pinkie Pie.

Anyway. Categories.

Crazy Person
The Crazy Person can not be the Mysterious Wizard if they're used as "The Stupid Comic Relief." Emphasis on stupid. They can still be funny. An example of this Mysterious Wizard is Pinkie Pie; their brains are wired in weird ways so that their actions make sense to them, and only to them, yet their seemingly random behavior results in actually accomplishing stuff in a way that makes sense in retrospect. Basically, they have to act crazy yet still be super competent. Pinkie Pie was not a Mysterious Wizard when she tried taking care of the Cake's babies, but she was a Mysterious Wizard when she drove off the parasprites.

Bad Guy
Usually, a bad guy who is the Mysterious Wizard will not be the main antagonist. Mostly because they're insanely competent and the good guys will have to convince them to stop being a bad guy. Boba Fett is an example of a Bad Guy. His 'death' (it's debatable as to whether or not he actually died) was handled poorly because he lost to random chance. Darth Vader is another one. An important point to note is that both characters stopped being Mysterious Wizards after we'd seen the prequels. After seeing them there, in the next three movies they weren't Mysterious Wizards anymore. If you're writing one of these, you need to avoid character moments like the plague. It's counter intuitive, but if you want to maintain their status you must do it. This boils down to the main point: keep them out of the story as much as possible. Otherwise, if they're seen too much readers will get salty that they don't have any character moments and then they also lose their status. These guys are insanely hard to get and keep right. Show a few scenes of them being competent, don't explain their actions, and stay the buck away from backstory. Remember Vader's line to Fett? "No disintegrations." That line automatically made Boba Fett a Mysterious Wizard. Stick to that kind of thing.

Gandalf
Conversely, this one is very easy to get right. Again, you can't explain their backstory too much or they lose their status. But you can let some hints through. You don't have to make them seem crazy. All you have to do is let them read your script, then demonstrate foreknowledge that they couldn't possibly have known beforehand. Gandalfs are named after the character in Lord of the Rings because that's the archetype. They can meet with the main character(s) multiple times, but—and this is important—you can't have them solve any problems that are too big. Gandalfs operate on "soft magic." That is, they're not explained. Limit their interactions to giving out ancient relics and quest locations. Personally, I try as hard as I can to avoid Gandalfs. With one of them in your story, you have no choice but to operate under a "soft magic" system and to some any appearance of the Gandalf will always appear to be a Deus Ex Machina.

Dragon
These guys are just there because they're cool. They're the Cthulus and ancient awoken gods of the story. Again, limit interactions with them to the bare minimum. Your characters will talk about the Dragon(s) like they're legends or gods. If you need a better example, here you go: Nightmare Moon before she came down from the moon. Limit their interactions with the world at large to one to three per book. Otherwise have them sleeping or just operating their lands or whatever. And always make every scene with a Dragon awesome. They need to be competent, wise, and powerful. Pulled off poorly and they'll turn your story into a train wreck, but done right and they'll add a nice dash of awesome. At its latest episode, MLP has no dragons.

Or the Mysterious Wizard can be that one crazy guy dressed up that looks as though he sells incredibly rare items, like in a game

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I'll have to remember that Gandalf personality for my fic...

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Celestia is a Gandalf most of the time by your definition.

Gandalf occasionally did stuff like fight the Balrog and Saruman. Celestia banished her sister, defeated Discord, and pretty much has been Worfed any other time someone would call on her to be a Deus ex Machina.

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Is Rick Sanchez from Rick and Morty a combo of Crazy and Dragon?

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You should do a "how to write the villain as an underdog". You're interesting enough to make something like that both informative and whimsically engaging.