Hmmm...
One might be able to combine a cheap sun sensor (two photocells with a vertical shade in between), some absolute position feedback information, and a basic free-running real-time clock chip.
The idea is that when the sun is shining brightly, the controller could easily find the exact angle of the sun using the sensor. Then knowing the date, it could update the real time clock against the exact time (with a sun-time to local time algorithm). If you have enough time to create the SW, you could even take it to the next level and predict the long term clock drift against ambient temperature.
Personally, I'd just use the cheap sun sensor (period) and move the array about twice an hour. If the sun isn't shining enough to find it, then who cares?
Maybe the sun sensor could even be fixed to simply find solar noon once in a while. As mentioned earlier, you don't really need time to the nearest minute to be close enough.
Note - it's probably not too difficult to consume a significant portion of your solar generated power with your control system. You'll be wanting to keep a very close eye on the overall average electric power consumption of the entire control and motion system. Turn it off at night.