Melanie,
Do you happen to know when the watch was last serviced?
Assuming it is water, then the watch may not be water-resistant anymore but the stains could also come from something else like an old gasket that is disintegrating or possibly some oil from the movement.
I am tagging
@Archer our resident watchmaker to see what his expert take is.
PS: beautiful watch!
EDIT: I was just checking your resent posts and saw that you posted about an experience with “Armstrong Watch”. What was that about!?