All of the v4 board series at least, but possibly even the older ones too, have the stepper cooling fan plug on the mainboard wired in parallel with the part cooling fan. The proper fix is to instead wire your own 2 pin JST-XH 2.54 socket pigtail onto the always-on screw terminal connecters in parallel with the always-on hot end's cooling fan instead.
This will make the 4010 fan that blows up into the bottom of the case run any time the machine is powered, instead of just when the part cooling blower fan is spooled up.
Links and stuff: