It's a large CPU cooling fan (model B35502-35), and at the term velocity 3600 rpm type fan, the cut out seemed right at max term, est 2800-3400 rpm, I need to find that on semi ADM1027 computer fan control IC. It's somewhere..
Well that the current consumption of the pump whilst running from the battery was 3A, and the pump did operate from the battery and yet not an 20Amp supply, thoughts are that the pump being inductive can be the role in the problem thus far.
However with the pump playing 3A off the battery and with only 1V drop from the supply with an 5R resistor... the supply with resistor state that the pump in that scenario would be near the 50R resistance whilst the battery at 3Amp then places the pump at around 4R resistance.
What gauge wire is assembled to the pumps common returning to the supply? if the gauge is to small, the voltage value can climb back from an inductive source and produce ramps.
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My views on that are limited as when it happened in the past, I just changed the common to an larger wire with the thoughts of current flow and voltage statement, being these devises rely on voltage value to determine their playing field on output only to note the current when it's being exceeded to respond only then to shut down.
Possible current drive, pump start, then sudden ramp back resulting in over voltage detection = shut down, directing back to your inrush current factor.
That was with an XBOX 360 power supply with protection that could not start up my X2, 500 millifarad caps from a depleted stage without auto shutting down. Never resolved that, just switched to an PSU with an external dual P channel driver and an comparator that when the cell was depleted, the charge was driven though the 50R resisted P-channel FET, then when 8V was reached the other non resisted P-channel switched on to direct drive.
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It a plug pack (if available) with and rating over 1 Amp can drive the pump even slightly, then again that : problematic : supplies output is not up to the task. Even adding a diode in series to the pump and filter capacitor after the diode across the positive/negative terminals onto the pump would not stand much chance.
:edit: added the reference to which supply I was referring to