According to my 1998 EVTM, this "auxiliary relay box #2" contains the blower motor relay, high speed blower relay, fog lamp relay, and front washer pump relay. The separate high speed blower relay bypasses the resistor when high speed is selected, but this only exists in the manual version of climate control. With EATC, everything is controlled by the blower speed controller. It's worth noting that in both cases, power to the blower is applied through the blower relay, but speed control is on the low (ground) side. If the OP's vehicle is equipped with EATC and he finds power present on both sides of the blower motor, the problem is with the speed controller (or rarely, the EATC itself). Because internally the controller box still has a high speed bypass, it's possible that the blower will work when commanded (or manually set) to maximum speed but not otherwise. That's what happened when mine failed, and it was quite comical: the A/C wouldn't blow any air until it got really hot inside, then the motor would kick in on high speed, cool the cabin down some, stop, and the cycle repeated.
Incidentally, it's simpler and cheaper to control the amount of current flowing through any device from the "ground" side, and that's why it was designed like that.