I am getting mixed information
Gimmighouls are scattered around the map from the moment you start the game, and none of them are allowed to be Shiny whatsoever. It's possible that Gimmighoul will only be available in his alternate colors through Pokemon Go, the same place in which he made his debut.
Gimmighoul is currently shiny-locked in Pokemon Scarlet and Violet.
For more information: https://primagames.com/tips/all-shiny-locked-pokemon-in-pokemon-scarlet-and-violet