Solar powered mini water pump: how to turn it on/off automatically
You don’t really need multiple solar panels, I would add a small battery, Perhaps lead acid for durability, and a solar charge controller to keep it at the proper charge level. You should be able to get all of this off-the-shelf. 

After that, just get an Arduino or a PI zero, and a relay shield or hat, the code to start once an hour run for a few minutes and then put the processor to sleep is relatively straight forward. And, although this is overkill and simpler circuitry could be designed to do this, it would require more experience that what you seem to have, it’s not necessary unless you are designing a sellable product, and it would save you a lot of aggravation later on. Particularly if you feel compelled to modify the behavior in the future. 

What you would need if you want to put together a circuit from scratch:


A solar charge controller. An IC such as this one, its purpose is to optimize power extraction from the solar panel. 
A battery or super capacitor. To store the necessary power to drive the pump and the rest of the circuitry. 
a small switching regulator for the circuitry power. 
A power switch, relay, or transistor to drive the pump. You might want to regulate the voltage to it unless you can directly power it from the battery. You can do this via simple pen and an LC filter, ourjust a simple switching regulator. 
A reasonably stable oscillator. A cheap circuit would just use an RC, a less cheap one a ceramic resonator, but a crystal oscillator takes all the guess work out of it. 
A set of counters and flip flops to put together a state machine with the desired duty cycle of 3mins per hour (a purely analog oscillator with such a duty cycle would be very hard to pull off). This is where I would use a timer counter IC, which are being discontinued. 


Such a system would be very hard to modify once put together unless the changes are designed from the beginning.

Or for less hassle and money you can use a simple 8-pin microcontroller (e.g., a PIC or a tinyAVR) with its built-in RC oscillator and program it to generate the duty cycle, the pump PWM, and even a heartbeat LED so you know it’s working, and go to sleep to conserve power. The same thing you would do with an Arduino, harder to program, but with no unnecessary parts and perhaps more satisfying.