According to our termite company, the new theory is that it is best to seal all vents. However, this can cause some problems, so they put an air inducer on the A/C plenum that allows a little bit of conditioned air into the crawl space, or if humidity is a problem, they run a dehumidifier in the crawl space. The air inducer can cause pressurization differences in the crawl space, so guess what? You may need a vent!!
We have had a humidity problem since the house was built in 2005. The contractor made some bad errors in sloping, and I actually had water running through the crawl space when it rained. Have fixed most of those problems, and I laid plastic sheeting over the soil, which made a big improvement. We just did some major landscaping changes to the flower beds in the front of the house this year. If that doesn't completely solve the problem, I plan on sealing mine. When I do, I plan to put in an air inducer (they cost about $100). As for sealing the vents, the inspector suggested I use rigid foam and seal it with expanding foam around the edges.
If it were me, I would seal the vents and check annually to see if there is a humidity problem. We don't have a rat problem, but did have signs of mice. Last year when I went under the house, found no signs of mice, but did pull out 7 shedded snake skins. This year, no signs of mice and no shedded skins, so I guess nature worked.
Not sure any of this will help you.