Glad to here that you found the cats home.
My neighbor has such a junky house we get mice every fall. I finally gave up and said we could get a cat to help with the problem. I think he is a dud. He only caught one mouse that I know of and that mouse was already dead in a trap that he brought to my bed side. Last fall I was in the basement when I saw a mouse run across the floor. I looked at the cat and he looked at me with a what do you want me to do about it look on his face. My son has tried training him with toys but he won’t chase anything. He must be closely related to Garfield. The only time he moves is when you are passing by his food dish. Then he will run up to his dish and meow at you for food.
Because your neighbors house is why you have mice ?