There is only one way moisture/water gets in there and that is from a backed up evap drain or the heater core. I have seen also where the hose connections, on the firewall side leaking under pressure and the coolant would actually spit out and follow the core tube into the box from the outside but that is a very rare thing to happen. Refrigerant is a gas, not a liquid. The a/c system is under pressure at all times, even when engine is off and and sitting. When the defrost is on, in order for the compressor to cycle to help with the removal of moisture in the air inside the cab, the refrigerant pressure must be high enough for the pressure switches to cycle the compressor. If you have an evap leak it just releases pressure till it equalizes and then it will be almost static till it does in fact leak all out. Coolant does not build pressure till the engine runs and starts to build very slight pressure just from the water pump moving it in the system but it needs to build heat to really get the pressure up there. There is always moisture in the air as well, so depending an the atmosphere in that box and the ambient temp, I guess there could be some "sweat" in there. But, that sweat is not going to leave a foggy film on the inside of your windshield. You may have mold in there though. Those a/c drains can cause problems and still look like they are dripping it all out on the ground. You say you can't see signs of the heater core leaking. The leak does not have to necessarily be at the outer edge for you to be able to see it. It can be inner core area and hard to see and also, be aware that the core is hot when coolant goes in and out of it and when you shut the engine down and flow stops, the wet that may be there then may not show by the time you get it apart because the hot core evaporates the moisture of the coolant and then looks dry. The smallest leak may never show till only when under enough pressure. Replace that core. Double check the housing for the evap access but IMO I would leave that alone if you can't get it open. Why look? Just for peace of mind? I get it but I would leave it alone for fear of damaging the case. Any you tube videos show how to just open the case for evap replacement? Look for numerous videos and then make the decision.