Can a carotid or vertebral artery dissection (no trauma/injury) be slow developing over a couple months, or is it always within a day or week maximum?

Yes and no: The mode of onset can APPEAR gradual when it is in fact stepwise, but even a gradually progressive arterial dissection tends to manifest suddenly when it reaches its maximum extent. You’ve asked a good question. The mode of onset of an arterial dissection is often difficult to determine exactly because they can be asymptomatic in the early stages.