I am an FO.
I am not invisible. In public, I try to present the image of the well groomed, calm, cool, confident, and charismatic pilot (after all, I represent my company, the mainline we contract with, and all my brethren). As often as not, when I am seen with my captain, passengers approach me with their questions. Maybe standing head down and acting invisible actually Caused you to BE INVISIBLE.
I am not redundant; nor am I a "tradition". I augment my captain by insuring he/she keeps the flight safe, legal, and prudent. After the dispatcher and the captain, I am the third person to review the release. While rare, errors can slip through, and I am the last line of defense. In flight, he seeks my input for weather avoidance, abnormality resolution, and efficiency.
I am not an autopilot. In nine years flying single pilot, I never once had the autopilot correct my mistaken read-back, insure my alternate was legal, confirm my fuel load was correct, complete my manifest, or support my decision when I had to talk to the feds.
Each time I fly with a captain for the first time, he gives me a cautious or jaundiced look. He has no idea what kind of an FO he is getting. I understand and don't take it personally. I just come in, do my job, and within a few legs he knows he has someone who can cut the mustard. He gives me as much responsibility and authority as is legal. After hearing my opinion, he may not always agree with me. That is his prerogative: he did sign for the aircraft. And until a captain does something Wrong or Unsafe, I will pop tall, salute, and carry on. But when I am faced with that one bad apple who does something really stupid, I will take it up the chain: I believe I have earned enough of a reputation, that my complaint will be heard.