There is not much useful interface information in the pump controller specs. A schematic of the controller would be nice.
Without the schematic, you could still monitor the state of the two switches with an Arduino.
With the switches disconnected, use a multimeter to measure the voltage across each of the switch input terminals as well as the "switch closed" current flow.
The results would be helpful in deciding how to connect an Arduino safely, without interfering with controller operation.
An Arduino could also monitor battery voltage, solar panel current, etc. without any connection to the internals of the controller.