2013 Camry will make a sound like the fuel pump is running. It’s not immediate when shut off but later when car has been sitting. It will stop if I turn the key on.

 

Is the noise from back of the car?

The car has a evaporator purge pump that can operate after the car is shut down. Its part of the fuel tank emission system. Normal

The owners manual would have something about this in referencing noises after the car is off.

 

 

Most likely the purge pump then. Normal.

The pump can come on any where up to 6 after after the engine is turned off.