It's just the drainage hole for the A/C condensor. The condensor and heatercore are both contained in the same boxed in piece. The water off of the condensor drains out that hole. When you say the A/C or heater is not in use, is the HVAC in the OFF position? If it's on DEFROST, DEFROST/FLOOR, PANEL VENT/FLOOR, or A/C the Compressor runs so you will get condisation coming from it.
I mean the heater is not on (105 out yesterday/ no hvac on at all) and ac has issues so it is not being used. Assuming then this means the heater core is leaking right? Can it be bypasssed for now till it cools off a little to work on it?