I am thinking that the motherboard must have been configured this way, and it is very rigid as there is absolutely no configuration available for the fan headers in the BIOS beyond viewing the RPMs for the 2 labeled 4-pin headers. That is all. It is a very limited "dumbed down" BIOS. And MSI will not provide any information as they say HP has this information, and HP cannot be contacted directly (unless you know a loop-hole about how to contact HP directly?)That suggests then some issue with PUMP_FAN pins 3 and/or 4.
Pin 3 = Tach/Signal/Sense
Pin 4 = Control/PWM
Because both fans work via the CPU_FAN header the problem is likely within the PUMP_FAN connection.
Any access to an additional known working fan or two to test as well.
Objective being to confirm, in some manner, that the PUMP_FAN connection is the problem.
Or that some other factor is involved.