Today, I decided to try and time-lapse it. I set up my tripod, got everything in order, and waited for the sunrise to begin. It started getting slightly lighter, so I started shooting at 1 photo per 8 seconds. Long story short, it was too cloudy for the sun to be seen at all, so the amaryllis pretty much stayed put. Even the slight movement you can see through the movie is due to heater vents blowing on it. I couldn't cover them well enough to prevent all movement.
See on Flickr
The moral of the story is, sometimes clouds are stupid. Oh, well.