Hi!!!
When I need to size the EGC from the fire pump motor control to the pump Do I have to size it based on the Short Circuit protection and table 250.122 or based on the size of the wire?
The supply conductors from the controller to the pump motor are sized @ 125% of the FLA of the motor. and this is the size wire you will use in table 250.122 see 695.6(C)(2)
Short circuit protection only, except as allowed in 695.5(C)(2) (transformers)
The service feeding a fire pump must carry indefinitely the sum of the locked-rotor current of the fire pump motor(s) and the pressure maintenance pump motor(s) and the full-load current of the associated fire pump accessory equipment when connected to this power supply
If you are supplying from a transformer pay close attention to the requirements in 695.5
Also pay attention to voltage drop requirements in 695.7 and remember if you up size your ungrounded conductors for voltage drop, you have to up-size the EGC. (250.122(B)
Lot of math to do when doing fire pump systems