I should also point out how I've been using stealth and perception so far just so that everyone is aware of how it works and can make informed decisions on what to do:
A character or Servant doing the "Scouting" action in a specific location will automatically detect the number of Mages and Bases currently in the area, but may still not successfully spot those Mages (Using Perception vs Stealth).
A character performing another action is usually busy with that so may not roll Perception unless the hiding character is tailing that character or otherwise is in a pretty close proximity.
There are exceptions to this, but essentially, if you wish to observe someone, it's entirely possible they might also notice you, but if you are simply getting they lay of the land and don't want specific information about someone or a group of people, you don't need to make a stealth check unless there are characters in the area looking for you or not doing any actions at all (which essentially defaults to a scouting action).
This means that sometimes doing a scouting action in your own base zone is a valid strategy as you both get to find out whether someone is in the area currently, but may even spot them in a perception check that you would otherwise be disallowed from if you were doing one of the other actions.
Hopefully that makes it clearer and gives you an idea of how I will be rolling your stealth and perception checks going forward. Keep your eyes peeled!