Air and heat only blowing out of defrost vents?

I pulled the glove box out and noticed black and white lines disconnected and just lying there. Is this the reason I’m only getting air and heat out of the defrost vents and if so, where do these lines connect to? I’ve attached a picture.

Need help knowing where the gray vacuum hose goes. I have air coming out all of the vents now so the mode actuator is hooked up, but my AC is not getting cold. Air before mode actuator was hooked up was cold or partially cold, intermittent. Now it’s warm so since the gray comes from the heater control valve, where does it hook up in the cab and does it shut off the heat so A/C can come on?

Does it hook up to the climate control panel as shown in picture? You can see there are 6 nipples on the panel but only a mold that was put on by the previous owner or it was factory not sure. Let me know if it goes into the climate control panel

All of the functions are working properly as far as fascia, defrost, and floor so the hoses that are assigned vacuum are getting it. I’m thinking the gray hose doesn’t go to the climate controls like the other ones do because of the factory plug in the picture I sent only accommodating 5 vacuum lines. Is it possible that the gray vacuum line tees off from the white vacuum line or the black since they are so close to each other? The black line is the main vacuum line and the white, according to the diagram you sent is an air inlet line. That being said, since the gray line, also being a vacuum line according to the chart you sent, shuts off the heater control valve so the air conditioning can work, would it make sense to say that the gray line should tee off from the white line? Sorry for the back and forth, Ford so far hasn’t been very accommodating to help fix this since I haven’t taken it to a shop.

Yes, so does the gray vacuum hose tee off of the white one that connected to the fresh air (defrost actuator)? That is where the gray hose is closest to.