And note Illengine said BARN cats.
You get them as kittens and put them in the barn in a cage with some of your old worn underwear but left unwashed so they bond with you.
You need a big cage, I used a converted childs play pen I got from the salvage store for $ 5
After a week of being in the pen, it gets opened but the cat is locked up overnight & only fed in side the pen in the mornings .
Gradually let it out more then when it is bigger than a rat, leave it out all night.
Give it a short name like Cat, Bob, etc and call it every time you feed it so it gets used to coming when you call.
You can train cats , it just takes a lot longer & more effort than a dog.
I keep a dish with some small chunks of lamb's heart next to me when doing bench work & occasionally flick one onto the floor .
This trains the cat to find whatever you drop on the floor , much easier than getting on your hands & knees with a torch.
A trigger sprayer with about 0.5% citruis oil in it works the same for cats as a rolled newspaper for a dog so when it jumps up on the bench a quick squirt will send it away.
The other biggie is to pull the blower housing off everything .
Mice do not like open roof dwellings