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There is a thin diameter pipe that comes off the small port on the water pump outlet and heads up towards the top center front of the engine where it T's. One part of the T is connected to the upper coolant pipe (the plastic one that joins to the infamous Y pipe).
A part number or even a description would be helpful.
I broke mine there once removing the oil filter cap. I temp repaired it (for three years or more) with a short piece of coolant hose and two worm clamps. Got the final repair done while the coolant lines under the supercharger were replaced.
No help with part number nor nomenclature though, just enough to get you back on the road for awhile.
It's called the radiator overflow hose and for a 2014 XKR it is part number C2P13304.
I replaced the equivalent part on my F-Type a few years ago, as you have found out it gets very brittle with age and heat cycles and is prone to crack.
Fairly simple job to replace just watch out for broken bits of it stuck where it plugs in to the upper coolant pipe, when you remove the old pipe this plug/connection will shatter and crack for sure!