I forgot to mention that in some cases if replacing a single AA battery as a 'battery eliminator' you would need native 1.5VDC out. Tiny 12V to 1.5V DC-DC converter do exist. Same idea for 12V to 9V battery. It looks like a fair number of the small ones I'm seeing on mouser and digikey are meant to be soldered onto a board as part of a larger project, but I don't see why they wouldn't work if soldered directly to a couple of wires coming from the 12V out of a poe splitter such as that.