Also with lead acid batteries, any charge voltage instructed without related temperature specification is meaningless. Charge termination / float / equalization voltages are all functions of temperature, and steep enough functions that it really matters to the point of any half-decent charger having a temperature sensor for voltage compensation. Car alternators have this (you can see how they output up to 16V on a really cold winter day, and 14V on hot summer day), decent UPSes do as well. If you use any random lab supply, you need to be aware of your lab temperature to maybe +/- 3..5 degC accuracy and find an actual voltage table from the battery manufacturer you can trust.
And generally, the fewer cells in series, the better chances of successful equalization without damage of "drying out". 12V pack already is internally 6s, but at least the cells are (possibly, maybe) better matched than two separate 6s packs (12V bricks) put in series afterwards. If stars align properly, you can series charge even higher voltage packs just fine, it's just trickier and more prone to errors causing premature failure. Cell-level (2V) battery management would be optimal, like in the li-ion world, but AFAIK literally no one ever does that on lead acid.