I would think you could wire up a 12 volt relay to accomplish triggering backup camera mode with a switch, while still allowing it to work when the switch is off and the car is shifted into reverse. Disclaimer: It's been a while since I wired up a relay, but if I remember correctly how they work, this should do the trick. Try this at your own risk.
Relay's work like a switch with a trigger to turn power on and off. There's also a pin to allow current to pass through even when the relay is off.
To provide the relay what it needs to function, you need to give it power and ground. You'd locate a 12 volt source that turns off with the car (so you're not powering the relay when the car is off). I'd probably use the power from a lighter plug that cuts off when the car is off. (On my CX-9, the dash plug turns off with the car, but the center console one stays on all the time). You could use the ground from the lighter plug as well. Connect the 12 volt power to pin 86 and the ground to pin 87. On one of these two wires is where you'll put your switch to toggle the camera. Personally, I'd probably do the 12 volt wire. Once those two are connected, you'll hear the relay click on and off when you toggle the switch.
Locate the reverse trigger wire running to the radio and cut it. You'll connect the side going to the radio to the relay pin 30 (output). The other side of that wire would connect to pin 87a (in the middle) which will allow the reverse signal to pass through as it normally would when you shift the car into reverse.
That leaves you with one pin left which you'll use to provide the alternate source to tell the radio that it should be in reverse mode when the car isn't in reverse. I HAVE NO IDEA WHAT KIND OF TRIGGER IT IS LOOKING FOR. It could be 12 volts. It could be ground. It could be 6 volts (my radio puts out 6v for the backup camera). Use a multimeter to locate the wire (I can't tell which it is from the diagram above). Whatever that current is, you'd get that from somewhere to provide the trigger source for the radio when your new switch is on which will activate the relay to tell the radio to switch to reverse input mode. If the radio is looking for 12 volts, you could use the same power from the lighter plug by connecting 86 & 87 together. If reverse mode on the radio is triggered by ground, you could connect 85 & 87 together. If it's looking for anything other than 12 volts or ground, you're on your own.
I haven't done this myself on this car, but once you have that wired up, I think it would probably work.
Anyone have any thoughts on this approach?