are you in the second junkyard or first? because if its the first you gotta find Rat kings key and borrow Tao for deciphering a coded cloth then after doing the next part that if explained is literally just a big spoiler you can eventually take Tao away and he will offer to take you to his home. (if you chose to set him free for real.)
if you're going for Tao's home the plates puzzle doesn't need to be completed that's only some gear and later content not yet in game, you just need to clear the tunnel at the entrance to the ratkin's territory and go forward and do a small interaction with the rat's stuck there and then after it check the area again and it should give two options of either leaving or staying but the leaving makes it say "hey you need Tao for this bit" which you then go to Tao in the day and he should have an option to take you to his home.