ETayrien,
I would start by replacing the bulb and cleaning the contacts. The speed of the blink will increase to indicate that the bulb is bad. To test it, you might want to just switch the right side bulb with the left and see if the right side now blinks fast.
Not really sure why it doesn't click off automatically. It could be a bad directional unit on the steering column. That might also explain why it clicks so fast. I would first start by chcking all the bulbs and connections.
Hope it helps.
Radioactive.