Coolant reservoir hose

Good morning,

I attached the removal and installation of the surge tank for you below. There is only one hose that goes to the neck of the radiator.

https://www.2carpros.com/articles/coolant-reservoir-replacement

https://www.2carpros.com/articles/car-is-leaking-coolant

Roy

If you mean the hose from the expansion tank it should attach to a port on the radiator below the radiator cap on the neck. Then there is the overflow hose that is on the tank itself, that is open and connects only at one end on the reservoir under the cap. If the hose between the expansion tank and radiator came off or failed it will get coolant everywhere.
In the third image the hose with the red line on it is the one that connects to the radiator port in the last image with the red circle. The yellow one is open. Which hose has coolant coming out?

Okay, the yellow one in the first two or in the third picture? If it's the one in the first two, the hose is split or damaged, replacing it should repair that. If it's the open hose in the third image that could be for a couple reasons, the first being the system was overfilled and now that weather is warming up the system is purging the excess. The other it that there is a bad head gasket of other cause of overheating that is forcing the coolant out.
Please clarify and we can go from there.

That could be the radiator cap not holding pressure and passing fluid into the tank. That hose is an overflow hose from being too full.

I would replace the radiator cap.

Roy

As Roy stated, check the cap to see if it's fully engaged, some can seem like they are tight when they are not.