Average time on site won't be accurate in your case because GA calculates it by subtracting time duration between two successive visits. In your case, it will usually be just single pageview so average time will be misleading.

May I suggest using getclicky.com which calculates time based on actual time spent.

Great! One more thought I had: also track whether the failure was due to the mouse or keyboard. When you have gathered a decent number of results I will be very interested to see a blog post with some nice graphs.

Now tracking fails (with the event type), and successes. If the data looks interesting I'll definitely write it up!

I'd discard results under say a second or 2, took me a couple of goes to see that you can't move the mouse at all once the page loads.

This achievement doesn't up my gamerscore!??!