The "Grey Man," you must become the grey man, you should act like the grey man.
This term describes the intentional act of dressing and behaving in an inconspicuous manner, in order to avoid any unwanted attention from strangers or authorities. The goal is to dress, walk, and behave as a local, without attracting any attention to yourself. To "blend in" in a foreign (usually hostile) enviroment. To be visible and yet invisible at the same time.
It is a term sometimes used by special forces or espionage operatives, in scenarios when an operative in the field must assume the disguise of an average, unremarkable local civilian. The goal is to use this disguise in order to travel unchecked through populated, urban areas whilst remaining undetected, and to avoid attracting any attention to himself or his real identity as a foreign agent.
"A pilot shot down behind enemy lines should act like the grey man: quickly don the garb of the locals, avoid eye contact, conversation, and children." (As they are more likely to point or shout when they see someone who is unusual or noteworthy.)
A wanted fugitive on the run from authorities would certainly want to become "the grey man" in order to avoid leaving a memorable impression on anyone who may recognize his face; they would be less likely to describe his appearance accurately if he is not particularly memorable.
"It was my first time in Moscow. I didn't speak the language very well and I didn't want to stand out as a foreigner, so I just decided to act like the grey man and blend in with the locals as best I could."