Mike would know more about the "innards" of these units than I do.
That being said, it seems to me that the fact that you can attach more than one head to each power pack is some indication that the heads themselves contain the thyristor.
In addition, I note that one of originally available accessories for the flashes was the "Power Pack N-20" which allowed you to run the heads directly from mains power, without an intervening portable battery pack. I'd be surprised to find a thyristor in an N-20.
One further thought built on Mike's comments - has the OP tried the other socket on the other side of the power pack?