Regardless of the point of this exercise, (shrug) here's how it should be wired, given that I understand the concept correctly. Note the changes to your diagram in green.
What you want to do it interrupt the voltage to the reverse light from the brake pedal with a SPDT (??) switch (ON-ON config) that has a 12V source connected to the other leg of the switch. The common leg of the switch carries on to the reverse light.
Note that all disclaimers are in place about melting wires, cops chasing you, your dog dying, etc, etc, etc.
Good luck....