well berkshire in a marking, not a color so she's always a berk
as for the color it sounds like you are describing a black rat that is rusting. blue rats will sometime do this too, i don't know if aqoutis can, i think some white can get dingy but i'm not sure if that is related to the coat or the cleaning habits of the rat.
anyway, back to what you are describing. your black berkshire is rusting. i'm not really sure why some rats do this and others don't or why it is not always related to the age, could just be the genetics, i don't know. but i don't think its anythign to concern yourself about. happens a lot of the time in black rats and i've never noticed a health concern for it. often i have noticed that it happens in older rats or gets more pronounced as the rat with the rusting gets older. so maybe it does have something to do with age.
anyway, as far as i know your rat is fine. just rusting. which is fine and normal for dark rats.