Need Heater Hose orientation for 1970 Ford Mustang 351 Cleveland bought in pieces

It's worth fitting the elbows as they stop any tight bends or kinks in the hoses. It also helps the heater core fit without any extra problems.

Aren't there hose clamps on the two hoses at the firewall? That hose should come off right there-one is connected to the heater core inlet inside the heater case, the other hose is connected to the heater core outlet tube. While you are at it, replace both hoses. Heater hoses are standard sizes, like only two sizes, larger is 3/4 " diameter. Take an old piece of your hose to parts store for replacement. They have rolls of heater hoses, can cut you off just what you need for low price.
If the hose clamps are not on the hoses at firewall, they must be accessed from under the dash, but should be easily accessible.
Really, a 1962 falcon? 50 years old and still going? That was the year I graduated high school, driving a 1957 Dodge two door black hardtop, yes, the big finned clown car-lol.

Pull the hose off the vacuum modulator
& see if it has oil in the hose

If so, replace modulator,otherwise it has to come
out & be rebuilt

It is a 3 speed,there is no overdrive

there is heater core bypass valve connected to the heater hose from the engine to the heater , check the vacuum actuator hose for leaks
( replace that vacuum hose is what i would do ) if you replace that vacuum hose and still getting zero heat output from the heater core .
then the heater core bypass valve is either jammed closed or failed completely

I would try flushing heater core to see if it's plugged. I don't think it's waterpump, your rig would be overheating if it was. Leaking is most common waterpump failure.

you have a blown head gasket. its over pressurizing the cooling system and blowing the hose.

That tube is the A/C drain port. Your problem is the heater core is leaking and draining from the A/Cdrain port. I hope this helps.
Thank You,
Roy

Go under the hood,, find where the heater hoses come out of the motor,,,then take a short piece of rubber hose and put it in a "U" shaped configuration thereby making the coolant travell right back into the engine and by-passing the heater core altogether.
If you do this correctly,,,then you will be able to add some water or better still "Coolant" and then drive home or to a garage.

possible clogged heater core

Sounds like you have partialy blocked heater core,not enough flow to the heater or heater tap either not working or only partialy open.You may have to remove heater hose at the fire wall and flush with garden hose.Also check if heater hoses are clear and running freely by using the same garden hose If you put hose up removed heater hose you should get a strong run of water coming out of the heater radiator.