I tried a plug and play Y cable in the front dash first and lost the wireless mic for the Bluetooth capabilities. Everything works with the full harness.
I did not have a backup camera at all. I installed a full harness from the tailgate forward and the camera works on non-entune radio. It took about 45 minutes but could be done in less time.
Yes, it's possible to install a backup camera on the 2013 Tacoma with a radio that is not an Entune radio system. You will have to run a harness from the tailgate to the front. It's not hard and only took me about 45 minutes to complete.
This is my first Taco. Shortly after buying it we were hit with two bad hail storms. It went to the shop for repairs and I just got it back after a month at the shop. I just finished installing the delay wiper control. Locking tailgate handle with the backup camera is next on the list...
It probably wouldn't be covered by the warranty if it was chewed by some critter.
I recommend taking a look yourself if they told you what part is, to see if you are able to tell if something else could have caused the problem.