"Battery drain" implies that the thyristor circuit somehow acts as an energy preservation measure. However, the primary purpose of the thyristor circuit is to accurately dose flash power by cutting short the current passed through the flash tube. It's a nice bonus that this can help cut down battery use, but I'm pretty sure that this concept was introduced primarily to allow for automatic exposure control, not energy preservation. The two go hand in hand, however.
The predecessor to thyristor circuitry was, IIRC, referred to as "quench" tubes.
In those flashes, the circuitry measured the light reflecting back from the subject and when the right level was reached diverted the energy from the capacitor from the flash tube to a quench tube, where it was merely dispelled/used up/wasted. As a result, each use of the flash fully discharged the capacitor, resulting in a lot of wasted battery power
As an example, the Metz 202 flash.
When they switched to thyristor, the not needed portion of the energy stored in the capacitor was allowed to remain in or returned to the capacitor.
The actual auto exposure measuring system was the same or similar - the switching circuit for the capacitor discharge improved.
That may have been incorporated in the Metz 402 - I can't remember. It definitely was incorporated in the 60 CT and 45 CT series Mets flashes.