The problem that I see is that the BRE2 was sold with the 4 pin Berg connector. Any that you might find now are several years old and likely on their way to battery heaven. It's a primary battery, so any source of 6 volts, be it a bunch of alkaline cells, or a camera battery, or whatever will need the Berg connector. Since the clock draws micro-amperes, any battery will last its shelf live. Plain old AA cells will work fine. Or scrounge a couple lithium packs from a vaping kit (unused, of course). Get a bunch of lemons and some copper wire and iron nails... A pair of CR2032 coin cells will work.
I guess that I'm trying to say that the source isn't terribly critical.