Weird popping sound when turning the heater/AC settings, no heat

The blend door works fine and it's not what is making the noise believe. I've had my ear to everything. I am waiting for the dealership to let me know when I can bring it in and they can deal with it because I give up. Thanks though.

I think it's a air bubble trapped in my heater core and no matter my efforts I can't get it out. So I hope the dealership can and I don't have to tear out my dash and all that to fix or replace it.

Do you know if the rear heater core will be affected if I bypass the front heater core? I am hoping by bypassing the front the extra little boost of coolant flow will kick the rear heat back on and I can live with that and maybe a heated seat cover until I have time to take the dash out and replace the front. Just tell me my theory is good to go even if it's not, because I'm about to just use it for target practice.

Thanks for the image, I should let you know I've been turning wrench's since just out of diapers. I have more tools then I can remember, it's like Christmas sometimes when I dig threw a tool box. :) I just haven't in all my years had a vehicle be as stubborn and mentally exhausting as this one. Go figure though it would be my truck instead of one I can just say I can't fix it and send it down the road. So I kind of need to figure it out.

So update: the rear heater core hoses get equally warm and only one hose for the front gets hot. I have disconnected the hoses at the T and it pissed out a good burst of air and then coolant. Still no heat, barely even warm. I jacked the front corner of it in the air until it was almost looking straight up at the sky and added a tall funnel and tried burping any air out, the only bubbles I saw were because I would give the top radiator hose a squeeze. I'm truly stumped, the popping sound almost like a couple old empty oil cans collided with a little bit of a hot running with all the keys going faintly with the popping. Almost like when I shut it off it sucks the water back from the core. And having no heat front or rear after replacing pretty much everything already, other then the cores it's all new stuff.
Oh, and this is my first Ford I own and it's really grown on me and dealing with 2 cores for heat is new for me also. I'll eventually figure it out if you or someone else doesn't beat me to it. I will definitely post what I find out when it's fixed. Thanks for your time and your ideas and all. I wish teleportation was a thing so people could just come and hear this thing and see all all the parts I've throw. At it. Or be able to teleport the truck to the top a steep mountain and start punching holes three it until it goes bang or something.