When I was a kid, a couple friends and I got together to write a circle story. It was a lot of fun. One of the characters had a bowler hat that he always wore. There was a really suspenseful moment in the story where he lost it. One of the other writers in our circle quickly made sure the hat was found.
Its funny how an object can help define a character. Fflewder Fflan's harp, from the Prydain Chronicles, comes to mind. The strings always break when he tells a lie, but since most of his lies are to hide how soft hearted he is, the reader loves him every time he's caught out. In Ella Enchanted, Ella is given a cup shaped like a howling wolf. The cup only appears briefly, but it's presence drives home how trapped Ella feels by her obedience curse.
Imagining objects for a character is a bit like Christmas shopping in the real world. When you really know the person you're shopping for, the perfect gift jumps out at you. It's so them that you can't resist buying it.