If you plug it into a different branch does the pump stay on? I wonder if the HDD is "stealing" power as it spins up causing the pump to momentarily shut off. If the drive is just a data storage drive it might drop into a low power "no spin/low spin" state and then when accessed spin up and choke the pump.
Another option would be to plug it into a external 12V supply (make sure you use one with enough power) and see if the pump continues to act strangely. If so, it's probably on the fritz and needs to be repaired or replaced.