Can 12V Batteries be made to act as a ±12V power source?
Just connect the + of one battery to the - of the other.  The point where the batteries connect is ground, the + terminal is +12V and the - terminal is -12V.



Of course, this is assuming the batteries are really 12V and not something more like 13.4V.

In that case you may be wanting to add a pair of regulators (a positive one and a negative one) or some Zener diodes to cap it at exactly +/-12V if your device can't handle more than 12V (unlikely).