Low power timer circuit for solar tracking
It seems you want to count hours, then look for RTC ICs (Real time clocks ICs). A common IC easy to use is the DS1307. But there are others ICs with better low power characteristics, here some suggestions:


ST
IDT


UPDATED: For example the DS1375 is a RTC with alarm, you can connect the output SQW/INT to a darlington transistor and this to the switch (relay). The duration of the square wave output signal must be adjusted to get the 11 degrees pro hour that you need. 
In this case the device must be configured via external I2C and to prevent loss the configuration data use a small CR battery.