Don't talk about rats! I am terrified of them. I once lived alone in a very old poorly built country house, miles from everywhere. There was a drainage problem and septic tank issues, workers had to dig out the back. It was soon after that I saw a rat. Sitting one dark evening, browsing on my phone and saw it fly past. After that landlady put down traps but the house had big gaps everywhere, and was a big house. The rats didn't go away and I saw they chewed lots of paperwork I put in a storage room and saw their droppings. Droppings are always a definite sign, as well as chewed things. It does sound like it might be a rat. Ugh!