They were NOT for use with AC in any fashion. These are battery operated only even though the plug appears (and is) similar to an AC socket, the other end of the cord was a female two pin connector for a battery pack or other type of flash. I have several types of cords like this, and our local camera store still caries a few styles of replacement. I have the auxiliary units and slave flash units that take some of these odd cords. With many, the insulation is rotting.
I never saw a battery eliminator as such back then. They did have big power supplies for studio use that these things could plug into. Usually though the studios didn't use flash bulbs, but they could accept the cords in the power units. Goodness, that goes back to the 40s.