There is a military term or idiom, which I cannot recall exactly, that essentially means calling negative attention to yourself. For example, you are doing something you know you shouldn't be doing. By asking the question, "Hey, is it OK to do this?" you get yourself in trouble; when if you kept your mouth shut, no one would have noticed what you were doing.
It had something to do with having a silhouette; it made me think of walking on the crest of a hill, where you could be easily spotted by a sniper, as opposed to walking with the hill behind you, so you didn't stand out. It's not "keep your head down".