Hi, I am so confused, hoping someone can shed light… In a nutshell, what appears to be a secondary condensate drain is dripping water outside. I understand that usually means clog in primary drain -- so I’m looking for where primary drain exits house, but I can’t find it, so I have no idea how to clean it out.

Now for some details…

Recently moved into this 7-yr-old two-story house, have run a/c only few times. Couple days ago, I had been running the a/c, and I was outside on side of house, and noticed water dripping profusely from a pipe above the kitchen window (pipe is between 1st and 2nd stories). Here’s a photo of that pipe:
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Googled, and started thinking this is a secondary condensate drain pipe that’s meant to alert us to a problem with the primary drain.

The Carrier indoor unit is located on 2nd floor, in a closet. Vertical positioning, with the return air coming from underneath. There is no visible drip pan. There are 2 pvc drain lines coming from the unit. One line (slightly lower) is on left, has a trap installed. What I assume is the secondary drain line (slightly higher) is on right, no trap installed. Both run out the wall, and I can’t see where they go after that. Also, unit has a sticker on it that says: “This unit is equipped with an AquaGuard condensate shut-off switch. If unit is not operating properly, check for condensate in drain pan or tray.” Here are photos:
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So, I’ve been assuming the exterior pipe coming out from wall above kitchen window is the secondary pipe, because why would they run the primary line to drip in such a conspicuous place all the time, hitting the window ledge and splashing water…

But the strange thing is, from what I can tell, there is no other drain outlet outside – it seems in researching online that the primary drain outlet is usually a pvc pipe near the outdoor HVAC unit -- and I’m seeing people use a wet/dry vac on that to clean out primary drain clogs.

But ours doesn’t appear to have one at all. I’ve checked around entire house, and the only thing resembling a pipe anywhere on the first floor is a set of two pipes, not pvc, built into the brick wall, and they’re behind the laundry room, so I’m guessing they have to do with washer/dryer? Here’s that photo:
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So I’m stumped. Where is my primary condensate drain line draining?... How can I clean it out if there’s no exterior outlet?...

Also, I just talked to my neighbor who also has 2-story house (he also has no obvious drain pipe near outdoor unit) – and he said that he too has a pipe on back of house, right above kitchen window, that drips water sometimes. So do I have this all wrong, and that 2nd floor pipe is actually the primary line? Am I worrying for nothing?

Thanks for wading through the details, and thank you for any help you can offer.