Reproduction disposable German 4.5V flashlight batteries. This flat type battery was used with many variations of flashlights and even in many bicycle headlights. These are built around brand new batteries and are not rechargeable or refillable. In testing, the batteries lasted over 12 hour of continuous use but did start to dim after about 6 hours. So it should hold up for several reenactments at least if you are using it normally and not as a lantern.
The art work was carefully restored and the ink will not bleed when wet. The battery has a black plastic case. Some may have slight errors (see last photo). The only other "flaw" is EXP written into the plastic on the bottom.
Flashlight bulbs are available here.