Backup warning turns off when car is placed in reverse

Check the fuse first, then: This is normally telling you that one of the backup sensors are bad/disconnected. That doesn't mean its a sure thing, but it gives you somewhere to test. Make sure all of the connections to the sensors are good and clean then, with key ON and engine OFF and car in reverse, listen closely to the sensors. The sensors should all be energized since that is why/how the system knows there is a fault. You will be able to hear a sensor ticking rapidly, but the locations really needs to be silent to hear it. When you cover the sensor, there will be an increase/change in noise, but it should still be a rapid pulse/click sound. If the sound doesn't change you have a bad sensor. If you never hear a sound, you'll need to make sure you have voltage to the sensors. If not, test the control module.