Autograph is an item in the “Unused” category (Key Items).
In-game descriptions
| Let’s Go, Pikachu! / Let’s Go, Eevee! · Sword / Shield | The autograph you got from the Vermilion City Gym Leader, Lt. Surge. He wrote, “Good luck!” |
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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