I would firstly check if there is power getting to the lamp properly.
Use a multimeter and check the terminals.
Even better would be the harness going to the lamp. The reverse wire should be Grey/White.
Also try and locate where the clicking is coming from, you dont need to fully engage reverse to try this.
You could have a faulty Reversing Light Switch.
But i would ensure that there is deff no power coming to the lamp before proceeding anywhere really.