I bought a brand new B2 a while ago as a hobbyist. Rarely used. I now have 2 batteries that won't take a charge. In other words, I have a boat anchor. It's completely silly for me to purchase 500.00 in batteries for the little amount of time I use it. They will just fail again when I want to use them. Do they make a clip-in accessory to be able to use these with AC power? If not, what do I need to purchase to be able to use these light heads on a new AC power pack? I'm done with the whole battery idea.
Chances are the batteries are just too low to trip the smart charge circuit. Often this can be overcome by connecting two batteries in parallel. In your case you might be able to use a 12v battery from a vehicle or other device, or a 12-14v power supply (e.g. laptop power supply).
The process is basically the same as explained in this Optima battery tech video: https://youtu.be/Slqd73ZOQvI
Sometimes you can just connect them in parallel momentarily and the low battery will take enough of a charge from the good battery/power supply to allow it to charge normally.
I am not aware of any means for operating the B2 system directly from AC power.