I have been trying to find out where exactly this location is. A Google maps marker or coordinates would be great.
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OK, It's called the Hite Crossing Bridge, and a Street View shot is available at this link that best matches the angle you have. It confused me for a bit as yours is using a long lens, but you can 'walk' down the hill and confirm it's all the same rocks, and in your shot you can just make out the Hite Bridge in the background, which is certainly the one at the location I have found. The photo is actually taken from a road west, looking down the canyon towards the bridge!
The reason it's so hard to find is that it's NOT on your Route 12/24, it's actually on UT-95. The site you reference has just used a picture from the state, but it's about 50 miles due east of Route 12, as the road crosses Glen Canyon, at the Hite Bridge.