Hey I have a question and a suggestion.
What's the timer for? I think you've talked about It before but i want to make sure what its used for. Is it like the game Amnesia: The Bunker where you use the timer item to know how much power you have for lights??
Also, you don't have to listen to me, but id highly recommend you don't let the pause screen freeze the entire game. The reason why is because this can makes horror games less scary or even worse, BREAK horror games. For example, I might be wrong on this but I believe in Resident Evil 7, whenever you pause the game, the old man can still hit you with his shovel. This is good way to scare players, because some players pause the game so they can stop the spooky moments. Also as I said before this can break games. This is why FNAF doesn't even implement a pause button. It's because if you have a pause screen in fnaf, then you can freely strategize on what to do without stress. Fnaf is about the feel of being distrait because there's so much you have to focus on at once under a time limit (AKA battery meter).
Now not every horror game needs to do this, some are probably fine without it, so It's a question you need to ask yourself as I'm not the one who's making... Our game. but yeah i would recommend you keep the pause screen, just don't let it freeze the game.