You have a couple of options, anonymous.
The easiest would be to use your gardevoir’s empathic abilities to detect the location of the ghost and determine what it might want. (It’s unlikely that you have a ghost/dark-type on your hands—that is, a pokémon who can resist your gardevoir’s psychic abilities—as most of those have clear, tangible forms, which means you would already know where it is.) Have your gardevoir follow its mental signature or its emotions back to the source, then either try to reason with it or use your mimikyu’s ghost-type techniques to draw it out into the open. Once in the open, you may wish to battle and capture it, or simply chase it out of your shop. (I would recommend capturing it, however, as letting it go risks amusing it with your reaction and thus encouraging it to return.)
The second easiest would be to hire a trainer or a channeler to remove the spirit for you. Of the two, the trainer would likely be the more desirable route, as a channeler’s methods can sometimes lead to unpredictable results, including more violent hauntings.
The third and possibly the hardest would be to acquire a pokémon that can use either Odor Sleuth or Keen Eye, both of which are techniques capable of locating or uncovering ghost-type pokémon, even when disguised. Use either of these techniques, then attempt to calm and reason with the pokémon (again, by having your gardevoir detect what it may want and then using a bit of verbal diplomacy to reach a compromise) or battle and capture it (by using either the pokémon who identified it or your mimikyu—or perhaps even both).
In short, the most important first step is to find a way to locate this pokémon and draw it out into the open. From there, what happens next may be a simple matter of befriending a pokémon, either by simply talking to it and helping it get what it needs or by battling it, depending on its preference or actual aggression levels. However, in my opinion, it seems that this ghost-type in question may simply be playing with you, which is why I say this part may be far, far easier than you would think—at least, compared to locating it in the first place.
Best of luck, anonymous!