I'm at the Eaton's apartment. I clicked on the magniflying glass on the lower left side of the poster in the front room . After I click the poster I get the big gear, but no key. Did I miss something?

In one path of the game - as Insurance Agent - you do not get the poster active.

See if the key you took from room 507 would work for you.

I already use the 507 key. Guess I have to start over or maybe from a previous save.

Move that cursor and maybe the active gear area is teeny.