Coolant leak. Please help with part names- resolved

Pertinent information as to what the car is.

Year 1996 Saab 900 SE

Body Style 5D / 5-door
Engine B204L 4-inline, Turbo - Petrol
Engine ID B204L5M20T057663
Gearbox 5-speed manual / Front wheel drive

We found a coolant was leaking from the car. The leek is not from the radiator. Neither the top or the bottom hoses.

The guilty hose exits from the um, engine block? It travels back behind the engine and enters into the firewall. So we think it is the heater hose? Please look at the hose with the red arrow.

This is where it is supposed to attach. These pictures were harvested from instructions of how to replace the engine. [url=https://photo.platonoff.com/Auto/20060518.Saab_NG900_Engine_Removal/?i=20060520k.Plate_attached.jpg[/url]
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Did I give it the right name? Anyone have an idea of how to find a diagram of where the hose enters the firewall? I can't see all the surfaces of the hose.

It sounds like a heater hose to me.
Does this help?
https://www.eeuroparts.com/Parts/5167/Heater-Hose-Kit-4961074/
It looks like the heater inlet and outlet hoses are supplied as an assembly, but they may be tricky to fit!

Is it split/perished or leaking at a connection?

Number 12 is the heater hose. I'm not sure on your particular year, through 94 the heater control valve is actually on the other side of the firewall. The hoses are the same, two that are clipped together. Same hoses cover many years.

Thank you so much guys! I have it on order, it's supposed to be at the store at 8 tomorrow. Here are instructions on replacing these hoses. Recommendations from folks who have done the job.

Some simple things to be aware of.  parts store hoses are often thinner or thicker than the factory ones.  So if these are held with spring type clamps a thinner hose will may not be pinched tight enough and come off or leak.  Spring clamps are the best answer if the hose thickness is the same.  But that isn't always the case.  The cure is to use a worm type clamp that adjusts size over a wider range.  The problem here is that modern hoses are sometime thinner and less elastic  and standard hose clamps are not elastic and modern engines that get hotter combined with the thinner rubber can sometimes cause problems.  Best answer is to use a worm type clamp with a built in spring.  Be aware these are pricey.(A pair of them might cost you more than the hose you are changing)  You also may not have room for them