Are you allowed to change who has the Leader Token at the end of the Mythos phase (as most other FFG games). Can't find any reference to it in the rules. I know you can choose during setup.

it might be using a similar rule as the “lead investigator” rule from the LCG game where the investigator is determined at the start of the game and remains the leader throughout.

Lead investigator, as far as I can tell, stays the same for the entire game. You do, however, get to choose what order you take the action phase and encounter phase in regardless of leader.

Leader only determines a few things like monster spawns, rules disagreements, and order that players draw from the Mythos cup/bag. There's really no need to change it other than monster spawns if the leader gets 'overwhelmed' but as far as I can see, you don't get to swap it around.

Ah, thanks Soakman, I'd missed being able to choose the order of the Action and Encounter phases.