Great to find this post.
I have a 2009 Elise and I now have the fast blinking turn signal issue. It was just the left signal at first. Now it seems to be both the left and right signals. I think all of the lights are working.
The fast rate starts as soon as the parking lights are turned on. So with either just the parking lights or with the headlights on as well, the blinking is about three times as fast as normal.
I know exactly what you mean about sitting at a traffic light with the turn signal blinking so fast. You immediately get the feeling that something is about to blow up.
The other day my left rear light fell out into the trunk and I put it back. A few months ago this happened too. But this time the bulb actually disengaged from the connector. The connector fell into the trunk and the blub was lying inside the rear light fixture. Maybe the bulb is just loose now? I'm going to check. I think it is the bulb that turns on when you put the car in reverse.