It is only when Cooper speaks with the fireman he does not wear the fbi-sign, and when he is dougie. It also looks like he does not wear it outside the motel, please rewatch the scene where Diane sees her self, cooper come out from the reception without the sign. I could be the darkness or my television, but i am pretty sure.
He definitly werar the sign when he is inside the motelroom with his strange behaviour.
The first time he shows up with the sign after "waking up", is when he arrive the basement at Great Northern with Diane and Cole, before he enters the mystic door.
Also in the glassbox he wears the sign
Well compiled.
The pin has to be some clue about the what and when of things, right? There's a lot of theories out there...
Cooper does not have the FBI pin from the time he leaves the Red Room through when he leaves the sheriff station. I think it's just the light at the motel not picking it up because he has it in the car and the motel room. In the Great Northern Basement through seeing Jeffries and "saving" Laura there is something there but not sure it's the FBI pin. He definitely has it once he is in and leaves the Red Room for the last time.
Fire walk with