If a player is called up for 13 games and sent back to AAA does his ML clock start?

assuming that he had never been up before, it starts when he comes up and pauses when he goes back down.  Also it's days not games that counts.  Slight caveats exists if he has previous ML service time.

Not sure what jfinn is inquiring about with his reference to "ML clock".

If he's talking about ML service time, then any regular season days spent on a major roster counts as ML service time and is accumulated.

If he's talking about the "option clock", then it starts the minute that he is added to the 40-man roster.  An option year will be burned in any season that he is on the 40-man roster and spends time in the minor leagues.