I've never seen brindle in rats, but I have oodles of brindle mice. I've got one right now that has classic bulldog markings--brindle body with a mostly white head.

I'm not 100% sure how it's inherited, but the brindling seems to be dominant in the mice I have. I'm getting brindle babies out of one brindle male from all colors of mice, even the wild type brown agouti females.