If your coolant is up to the full mark, when the motor is cold, someone needs to help diagnose your problem.

Unless the hose is getting weak???

 

Found this, might be a good direction to go in. It appears that when the car cools off, the antifreeze contracts and it should replenish its pressure back from the reservoir, but it can't creating the vacuum evidenced in the hose.

A bit long video, but just forward a bit:
This one goes into what is going on with hot / cold cycle, informative. At least it proves my system is not leaking a bit:

 

Maybe the radiator cap is bad- there is a check valve to let air back in when things cool off and shrink. Or maybe the problem will stop after a while, after all the air is out of the system. Trapped air may be expanding when hot, causing air in expansion tank to bleed off, then when cold it shrinks and tries to suck in more air through the cap. Or if your hose is old it may be too soft and ready to be replaced. I suspect the supply line is also doing that (hard to see). You can bleed off the air by removing the bleed screw by the cap, normally done when filling up with coolant.

 

So I ordered a Jaguar OEM cap from Harper Jaguar (~20 dollars with shipping) and I am noticing the hose is not sucked in anymore, so maybe the air is working its way out. So thanks for the right-on replies.

Question, there are two appendixes in the air intake pipes, one post-filter and one pre-filter. I want to get rid of both and picture them below. I want use the space to install a Champion coolant filter and run it for a year or so. I would provide my own hosing preserving the factory hosing to later reinstall it. Promise to let you in on it with pictures. I don't like those flakes in the cooling system, though they seem to have disappeared, hopefully not into the heater core.

what's this mystery box?

and this one?

 

Steel Seal? We all know better.