Aren't things like that programmed to not be shiny or is that just the event distribution pokemon?
Well it's (the SEP) given to you in the game as a gift Pokemon like Eevee, it's not from an actual event like the PCP so it might be possible to get a Shiny version, idk, I don't really know much about them. I don't have the patience to try though otherwise I'd test it out.
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