Not sure what a “pump start” might be. My pump has a large accumulator so pressure is always available even with all circuits off. I measured the valve output at the Rachio controller connection and got 7 Vdc @ 50 milliamps. I could build a simple circuit using 1 Amp 50 Vdc Schottky diodes (1N4001) that would allow groups of circuits (up to three) to be activated by one of the unused circuits without backfeeding any individual control.
