To some extent it really is a mixture of both. A Game Master is someone given a title in your game and it doesn't really matter what position they hold. When something goes wrong, players will turn all their attention to any Game Master they see. They don't even have to have any powers, you could just make someone a Game Master in name and that would be enough to start causing problems
Now generally, there is nothing wrong with some kid being a Game Master, but if he makes a mistake or if people don't agree with some action he undertook then they may construe that the belief it was because he was immature. Note that even a powerless Game Master has the power of words and all he has to do is just say one wrong thing. Also keep in mind someone just coming to the server may already have a negative preconception of young Game Masters which you can't help but you can avoid if you don't make someone too young a Game Master. If someone is older then people will naturally and stereotypically respect them more; especially if they are a Game Master.
This isn't to say that you should pick anyone to be a Game Master. Common sense is also important, as is work methodology and the ability to work under pressure. Though in hindsight of my own experience, these matters tend to be less important to the makings of a good Game Master then the personal facts about the Game Masters themselves. If the person is an idiot, then they shouldn't be a Game Master, else anyone with some ability to follow a rule set handed down by a Admin can follow that instead of making a decision based on his own common sense. A Game Master that actively shows up, does his work, and helps keep the server running smoothly is great; if they fail to get on the server, aren't doing any work, or are impacting the server operations then they probably aren't a good fit for the position. Sometimes s*** hits the fan and a Game Master might lose his cool, I doubt anyone would get seriously mad at this unless the Game Master has some anger issues or something really damning.
Of course, everyone who applies for the job should be tested for their qualifications. Ample time should be taken and there shouldn't be some prescribed time limit given - the intern Game Master becomes the full fledged Game Master when the Admin believes they are up for the task. This doesn't mean they should be kept in limbo but the relationship between the Admin and his Game Masters is far different then the relationship of the Game Master and the players on the Server.