Not exactly what you're asking, but it seems that you could add a physical momentary button or switch to the Reverse signal line on the unit to fake being in reverse gear. According to the manual, the display unit automatically switches to the camera view when the Reverse gear is selected. I don't have one connected, so I don't know that this would necessarily work.
Ideally, get a double-throw momentary button. Connect the HU's reverse wire to the "common" lead of the switch, and the vehicle's reverse gear line (backup lights feed/whatever) to the "normally-closed" lead of the switch, and a twelve-volt (fused) feed to the "normally-open" lead of the switch. As such, when the button is NOT depressed, the unit behaves as normal: if you shift to reverse, the signal from the vehicle feeds to the HU reverse line, which does the appropriate thing. If you depress the button, twelve volts feeds to the HU reverse line, so it thinks it's in reverse regardless, and acts like you shifted into reverse. When you release the button, it all goes back to normal operation again.