My headcanons about Tate revolve entirely around having a more active peripheral awareness of the weirdness of Gravity Falls. Of knowing kind of what happened to his dad, and having vague memories of “Stanford Pines” that don’t match up with the current owner of the Mystery Shack, but still not going there out of principle. That building makes him feel wrong, down to his core. Him making up with his dad after Weirdmageddon and trying to make up for all the lost time and hard feelings between them.
They also revolve around Tate not quite ever forgiving Ford for his part in his dad’s downward spiral. Despite saving the town, despite knowing his father forgave Ford, Tate doesn’t really let go of that anger for the scientist. He’s on good terms with Stanley, finally knowing why he had felt weird towards the Shack and the owner for years, despite not really disliking Stan himself. And having more than a few issues because of that dislike Tate has for Ford.