exhausted, out of
歇 centers on being completely drained or used up: exhausted, out of something, or having nothing left.
歇 combines 曷 (historically associated with stopping or ceasing) and 欠 (open mouth, often related to breath or lack). Together they suggest running out of breath or energy, leading to exhaustion.
The left side 曷 looks like a person gasping under a sun, and the right side 欠 is a person with an open mouth. Imagine someone so exhausted they can only pant, completely out of energy.
For ケツ, picture someone so exhausted they can only manage a weak 'kets' sound, like a deflating balloon: kets -> ケツ.