How to make +12v standby power from ATX power supply?
No, you can't; that's not how power supplies work.

The "negative" part in all your voltage rails is the same voltage, actually even connected, so you can't connect them in series.

For that to work, these individual voltage supplies would need to be isolated from each other. The opposite is desirable within a PC: you want all voltages to be relative to the same chassis ground voltage.