Can you trade the Patty wagon and the deputy's revolver then?
Yes. Those are specifically called out as Items in the rules (p. 16 under "Insane or Unconscious in an Other World"):
Important: When adding up items before discarding
them, count all Common Items, Unique Items, and
Spells. In addition, the Deputy’s Revolver and the Patrol
Wagon both count as items. Allies, Skills, and other
cards do not count towards this total.
Though it is under an unrelated section, they are defined as Items. Items can be traded. So that is the same definition I think is lacking with the Great Seal and White Ship. But if they ever FAQed it to be Items as well, I could understand it.
Best to agree on how you want to treat it and just stick with it in all your games.