I am not sure about Expeditions, but when the heater core on my Jeep Commander leaked it was on the passenger floorboard, you could smell it inside and you'd some steam coming out of the defrost vents indicating the coolant was getting on the core itself. Luckily on those there was a shortcut under the dash to do it
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I just replaced my thermostat and water pump on my 2016 this week. I took a couple of evenings to do it going nice and slow (personal reasons, my master mechanic dad isn't around anymore and it's the first thing I've had to open up mechanically since he passed) but looking back, I think the book calls for 3.5 hours of labor and overall I was a couple hours shy of it. I have better luck with metal impeller water pumps, and that was $75 retail at AutoZone. Ford OEM with plastic fins is $100 on rock auto, but that's preference.
The tube the tech got stuck on was the crossover tube that runs from the thermostat housing to the rear and is sealed by orings, slightly fudgey to get in place. If it's leaking passenger side at the rear I'd bet either an oring tore or he didn't confirm the rear oring was in tact.
The hoses for the heater core should either go straight in or are in a tbox there at the firewall, sorry I haven't looked yet.
I've also come to find out there's an auxiliary water pump on these, but I haven't looked into where yet. My wager is it's at the crossover pipe in the rear though, I'd certainly have them take it back in and reexamine that crossover pipe and the orings, especially since this occured right after they serviced it.
The pipes on my 2016 were not brittle but the driver side that goes down by the fender well was a turd and we dropped a socket in the frame when it came off haha
. That took a minute to fish out. If you take your time and analyze each piece as you do it and don't drink (lol) you'll be able to save each clip and screw.