Enigmatic Card is an item in the “Plot advancement” category (Key Items).
In-game descriptions
| Sun / Moon · Ultra Sun / Ultra Moon · Let’s Go, Pikachu! / Let’s Go, Eevee! · Sword / Shield | A mysterious card. Written on it is a request for you to go to a guest room in an Akala motel on Route 8. |
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Where to find it
Not placed on the atlas maps (so far: Red/Blue and Generation 3).
Sources : PokeAPI (items, item_flavor_text, machines) · atlas · pokeemerald species_info.h