Even if you get the schematic I think you have little chance of modifying it to give +/- 12 Volts at anything near 1 Amp. The transformer in a switched mode power supply is a key part of the design.
For low very currents you could make a virtual ground at the middle of the existing 24 Volt output using a couple of low value, high wattage resistors. For higher currents you would need additional active circuitry and power transistors. Think about it. If you are taking 1.5 Amps from the +12 side but close to nothing from the -12 side, the overall 24 Volt output is still giving 1.5 Amps. That "extra" 12 Volts and 1.5 Amps has to go somewhere as 18 Watts of heat.
I suggest you just go on ebay and buy a couple of those modules like in the attached photos. The 12 Volt 2 Amp one is £5 delivered in the UK. Less then US$15 for two?