by non magnetic, I don't mean that it's not permeable. I only used that word to indicate that the piece of metal is not a magnet in itself.
It is just a very flat piece of permeable metal about W1mm, H3", L2cm. It will attach itself to the magnet on both sides when placed on the magnet on it's flat side. But when I hold the bar loosely between my fingers and hold the magnet over it, it always flips to the same side every time.