Difficult to see exactly how the two cock-settings work, but if the pump's closed-off when the coolbox line is open, then you might have popped the diaphragm
or broken the linkage, by trying to suck against a vacuum? The simple way to test would be disconnect the line to the pump from the seacock, stick the end of it in a bucket/bowl of water
and see if it works, if it does, your problem may just be a partial-blockage in the skin-fitting (barnacles?).
That said, we had the exact same pump on our last boat and whilst the freshwater one worked fine for eleven years, we had two seawater-tap ones die after about three years each - the internal springs and linkage corroded; if that's your problem, you might well be in the right location: In both Greece
there were virtually identical pumps on sale
branded 'TMC' and their cost was less than half of the Whale version - little more than the cost of a Whale service
kit! More importantly, they seem to be more corrosion
resistant; we fitted/used one on that boat for a further five years without another problem and the one fitted to the seawater-tap line on our current
boat's also still going strong after five years.