I recommend explosives myself. It always solves whatever problem I have.

If it dies in your roof, it will rot, then smell, then maybe stain if youre unlucky.

You're think something got in and you have to get it out to solve the problem. Animal needs water and food every day and probably not getting it in the space you show. Figure out (from outside) how to exclude them from getting inside.

When we had mice I didn't want to have the hassle of poisoning, or the stench of rotting carcass.

So I built a DIY bucket trap, I got the basics from a yt channel. It's pretty easy, it's basically just a tunnel with some peanut butter at the end of it to entice them, and it's got a long'ish trap door that's activated by the weight of the mouse, and it's got a tall'ish bucket underneath it.
The bucket is tall to stop the mice from jumping back out of it.
Once we caught the mice we would drive a few miles away and let them go. They can find their way back if you release them too close.

After our third mice invasion I bought a cheap solar powered security camera that activates with motion. I put the camera on the ground where I thought the mice were travelling and getting in... and waited.
Then moved it periodically to find their trails and fine tuned it to find exactly where they were getting in.
Which was through an old outbuilding, then up a timber frame and through a hole in the soffit and fascia.
I sealed up that hole inside and out and never had an issue since.

If you just kill the mice (and it is mice, not mouse. There's pretty much always more than one) then the next lot will just kept on coming in. It'll just be mouse carcass on mouse carcass up there.
Blocking their way in is much better than killing them once they are in.

Dont forget poison can enter the food chain and have harmful effects on foxes and birds of prey. Have you tried calling summoning an owl?

If you have branches from a nearby tree touching your roof, that's how they got in. Mice climb trees. Always clear branches away from buildings.

I couldn't imagine living back in the day when you couldn't seal up a house. God I hate mice.

If you have a friend with a cat, see if you can borrow it for a while. Not to catch the mouse but to scare it away. Just the presence of cats makes them not want to be around. I moved into an apartment one time and saw a mouse before my cat moved in with me. I bought one of those catch and release traps but it never showed up again after my cat moved in.

That's how you end up with a smelly dead mouse in your ceiling.