How to wire in an alternate light controller?
The wiring you show will work.

However, connecting the outputs like that means even when the controller is switched off, its output might be hot.  Depending on how it is connected and enclosed, that may or may not be dangerous.

It might be better to use a double pole double throw switch wired so the input and output hots get switch between controllers and the other controller is completely disconnected.

And of course you have to make sure the switch is suitably rated for the max current and voltage of the circuit.

The neutrals should all be connected like you show.  Presumably your controller uses a separate power source since it doesn't have a neutral connection.