So, we know the Grand Inquisitor got incinerated and died in Star Wars Rebels as we see here...

But, the next time we see him is he is a temple guard in season 2...

However, in Rebels recon, it was confirmed that this was just a vision conjured by Yoda. Next time we see Grand Inquisitor, we see him as a spirit trapped in a Jedi temple on Tempes, confronting Luke Skywalker.

This was confirmed to be the real spirit of the Grand Inquisitor, yes, this comic is canon. So I heard a lot of people using the Revan from the old canon theory, like, "Oh the Grand Inquisitor's spirit split in 2 like Revan. One is the Light Side spirit that Kanan met and the other dark one is what Vader is keeping in the comic." But I have a different theory. So I think that after the Battle of Yavin, Vader somehow found this mysterious force artifact that allowed him to go back in the past to the moment of the Grand Inquisitor's death. As soon as he incinerated and died in the fiery electric pit, Vader grabbed the Inquisitor's spirit and took it with him to the present day, after the battle of Yavin. So basically, Grand Inquisitor time traveled. After going into the future, Grand Inquisitor's spirit was tied into an abandoned Jedi temple, preventing him from passing on to the afterlife, the Netherworld of the Force. Through a ritual, Vader made the Inquisitor`s spirit a fiery ghost that can make contact with the physical world. Years since, he haunted Verla, and later Luke Skywalker, as we see in the 2020 Canon Star Wars comic. I believe that after Vader died, the Inquisitor's spirit was free from the binds of the temple, but still has to remain a fiery ghost that can make contact with the physical world. I think he will show up in Mandalorian seasons 3 or 4, or the Ahsoka show, and then, he somehow, probably through a good person, learns the Light side of the Force once again in the Mandalorian or Ahsoka show. Eventually, his sprit is freed and passes on to the he Netherworld of the Force. He, however, learns to become good, and he becomes a good light side ghost. He chooses to remain in the physical universe to help people who he wronged, such as time traveling in the past to help Reva survive getting stabbed by Anakin and healing her. Then, I believe he helped a lot of people he could, except for one, Kanan, his former enemy who caused his death. So he time travels to the year 3 BBY helps Yoda and travels, into the Lothal Jedi temple. He knights Kanan a Jedi knight and defends the temple from Fifth Brother and Seventh Sister. After that, he finally becomes one with the Force, completing his redemption arc. This is what I think happened.