It was an ambitious idea, but I knew I wouldn't be returning to this place any time soon, so I had to do it. I spent the entire day before calculating the number of pictures I'd need to take to get a reasonably lengthed video at 24fps, the interval between the pictures, the azimuth of the sunset and the sunrise to figure out exactly at what angle to aim the camera, where to take the timelapse from, and all the logistics of having to rotate my three batteries between being in use and charging.
I decided that I would take around 3,000 pictures, each 14 seconds apart, to get a video of two minutes in length. It ended up actually being 3,380 pictures and 1:55 long.
I picked a spot just over the edge of the canyon at a point of the rim that extended into the canyon a few hundred feet. I picked it because the view was good, and more importantly, the camera could not be seen from the main viewing platform or almost any other point along the rim. This meant I could abandon it for lengths of time without having to greatly fear for someone stealing or tampering with the camera. This also meant that when I had to attend to the camera to adjust exposure or change battery, I had to climb down about six feet to a ledge no larger than a tabletop, beyond which was a drop that was not survivable. Excitement factor.