Not sure if this headcanon has been touched upon before, but it kinda piggybacks on the whole “Lewis being afraid of Arthur for a while” thing.
I imagine that Arthur was afraid of Mystery for quite a while after the cave incident (he got his ARM ripped off by what he thought was a harmless little dog, after all). And if we’re going with the ideas that only Arthur is aware of Mystery’s true form and that Mystery himself cannot speak, just imagine…
Vivi visiting Arthur in the hospital as soon as she hears the news that he’s awake. She decides to bring Mystery along to help provide comfort.
Arthur having a massive panic attack, because now all he sees in Mystery is glowing red eyes and a snarling maw stained in his blood.
Vivi being escorted out of the room while the nurses deal with Arthur. She’s standing in shock and confusion to his reaction. As far as she knew, Mystery was one of the few things that could calm Arthur.
When Arthur finally returns home, he spends the following months utterly terrified of Mystery. He’s unable to even be in the same room as the dog without breaking down.
The whole time, Vivi has no idea how to help, because Mystery was always what helped.
Eventually it gets to a point where Arthur realizes Mystery is no longer an immediate threat, but he’s still overly cautious when interacting with the dog (whenever he gathers the courage to do so).
When Arthur gets his prosthetic arm working properly, it’s the only one he’ll use to pet and play with Mystery.
By the events of “Ghost”, Arthur has mostly overcome his fear, but I imagine he still gets really jumpy if Mystery moves towards him unexpectedly or his muzzle gets a little too close for Arthur’s liking.
When Lewis rejoins the group, and he notices the ghost’s eerily similar behavior around him, Arthur starts to feel guilty for still fearing Mystery. At least Mystery didn’t kill him…