The smallest water pump that I can think of for you is this one:
It seems to be a BLDC (brushless DC) motor, hence durable. It seems to be 250LPH, which may be sufficient (confirm this). You can use a 12V solar panel, connect it to a 12V charge controller and battery to run the 3.6W pump. The charge controller takes input solar panels, regulates voltage to batteries and gives output to the pump. It can cut off when the voltage of the battery drops below 10.4V.
I have a 500W solar system and based on my experience, I can give some numbers for you:
The above 3.6W pump will consume about 86.4Wh per day. A 25W solar panel can generate about 100Wh per day during sunny days. But during cloudy days it can generate only about 25Wh or even less if your sky is dark and overcast. Hence if you want the system to survive through even cloudy days (which is common in Bangalore), then you better use a 50W solar panel with a big battery. For battery, you can use a 12V, 40Ah Exide solar tubular battery(minimum size available), which will store about 480Wh of energy, that will give you about 4 days of reserve power. The large panel will help your system to quickly recover from dull days of solar power supply.
But then I'm just hypothizing for your situation based only experience, so you will need to experiment and learn, especially during cloudy spells
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