The History of Time, Leofranc Holford - Strevens, (Oxford University Press (2005) p.101) has the following rule:

"A 13th month is added, under current rules, in years 3, 6, 9, 11, 14, 17, and 19 of a Metonic cycle nine years behind the Western 'Golden Number' cycle; the month repeated which must not be a winter month (1, 11, or 12), is that throughout which the sun will remain within the same sign of the zodiac, subject to the rule that the equinoxes and solstices must fall in months 2, 5, 8, and 11; if this would be breached, intercalation is postponed till after the second month of the following year."

I have not found Holford - Strevens to be a particularly reliable source. 86.173.166.100