Most backup cameras made in the last few years will have some sort of IR capability. The problem is, you just can't see as far as you can in the day. The reason for this is two-fold. First, the LED illuminators just don't put out that much light. Second, there needs to be something back there for the light to bounce off of, and get back to the camera. So, when backing into a carport, or seeing your toad, you should be fine. But, since the illuminators only have an effective range of 20-30 feet unless something is very close, you just can't see it.
To address this I can think of a couple of options...
if your only concern is seeing what's behind you when you're backing, install a couple of driving lights off the rear bumper. Switch them on when you back up. My coach has a pair of rear-facing halogen "docking lights" that really help.
You can also look for a pair of IR Illuminators:
https://www.amazon.com/s/ref=nb_sb_s...in%2Caps%2C565
But, even with the best illuminators out there, you're not going to see at night, like you would during the day...
To test if your current IR LEDs are working, many digital cameras are sensitive to IR light. Check your camera by pointing it at a TV remote while holding down a remote button. If you can see the LED at the front of the remote flashing on your camera screen, your camera sees IR. Just use it to look at your backup camera (with it powered), and you should see the LEDs lit...
Good luck!
Carl