What are these 2 hoses below Heat Control Valve

[DocuDude]

Ok,

Replacing HCV and nearby hoses.

What are these 2 hoses?
They are behind/below HCV.
One goes into fire wall, other goes down along firewall.

I cut them off cuz they looked leaky.

Here's the 2 hoses still attached to car (pic #1)
Here's the long plastic piece (I dont know name) they were attached too. (pic #2)

 

[Landseer]

The lines that go into/out of the firewall are for the main (front) heater, the 2 lines the go down the firewall are for the rear heater. Good pics of rear heater lines here:
bypassing rear heater hoses?
and
Heater lines cracked and leaked out all my coolant

 

[DocuDude]

So these are the Firewall Heater Hose...the FHH?
Wow!
I sliced em, now I gotta source them.

 

[DocuDude]

Slept on it, even more confused what these 2 hoses are called.
Here's the diagram with both hoses having arrow pointed at it.
The bottom hose doesnt have a part #.

What are these called?

 

[DocuDude]

Alright, so to help the next guy down the road, this is what I learned.
Thanks again Beno and other Mud members!

The top hose that goes into the firewall cannot be purchased from Toyota, unless you buy the metal rear hardlines that come with it.
However, it can be replaced with the 9556-31000 (cut to size)
(pic with blue arrows)
And the lower hose, same thing, hose can be purchased & cut...Beno says 5/8"
(pic with blue arrows)
-------
And the right-angle hose on the PS near the firewall...that comes out below the plastic T....use Gates 1/2 in. 90 deg. hose 28460
(pic with yellow arrow)