Oh, I seal those up with something more solid like rubber grommets where possible, or expanding foam covered with a rubberized coating etc. (I don’t like leaving expanding foam uncovered.) Once dry, I trim the foam so it looks like factory before rubberizing it. Done right, it should look original.
I’ve been using that method forever, and never had anything breach it. Screens or steel wool are for where you still want air flow, which in most instances you don’t.
BTW, if you’re going to frequent places where you might have rodent problems, LED lights under the hood, and under the vehicle will usually keep them at bay. Some people put the ones underneath on motion sensors. in the engine compartment, mine are on constantly if I turn them on, because rodents love to chew up the wiring.
"Always avoid expensive solutions to cheap problems." ~ OffGrid