I agree with the hose to the overflow or the radiator cap being the problem.
With the coolant pump not pumping (engine off) these are the 2 likely to cause this aside from very rare exceptions. The thermostat wouldn't cause this, even if it is completely shut and doesn't have a bleed valve the pressure could still equalize through the radiator and the rest of the system.
As the coolant cools it shrinks and needs to pull coolant from the overflow to take its place. If there is not coolant in the reservoir it should still pull air, which is not good but the hose still shouldn't collapse. The components involved are the radiator cap, overflow and hose.
Radiator cap - most commonly has a seal at the top, a sealing surface held by a spring to set the pressure (also allows expanded coolant to reach the overflow) and at the bottom center of that it has a little one way valve. This one way valve is what allows coolant to return from the overflow jug, if this is stuck it could lead to the radiator hose collapsing.
Hose to the overflow - if there is any restriction or blockage or weak spot where it could collapse under light vacuum - it could cause the problem.
Overflow - blocked or restricted passage could cause this. When this presents in the winter itís a good idea to check for ice, water may have been added to the overflow tank.
You can check for clear passages and lift up the one way valve on the cap to check if itís stuck. If you see it collapsed again you could pull off the hose at the radiator and see if the hose fills, this will tell you if itís in the cap or elsewhere. I'll try to the reply shorter next time.