24 V to -1.25 V and -12 V Converter
I'd be tempted to use a switching inverting regulator like this one: -



Then I'd derive -1.25V from the -12V output. The question showed 1A linear regulators so I'm assuming 2A is going to be enough to power the -12V and the -1.25V.

Should a linear regulator be needed on the output (less noise and usually cleaner) then use a "low-drop-out" device and run the switcher with an output of maybe -13V to power the linear regulator.

You can use the same chip to directly produce the -1.25V supply. It expects to see 0.8V on the FBX pin so choose the resistor divider appropriately and see how low this circuit can stably produce a -1.25V output. You might need to raise the inductance of L1A and L1B to more like 6.8uH though.