broken piece of jade
玦 centers on a broken or incomplete piece of jade, often specifically a jade ring with a gap or a fragment. The meaning is narrow and concrete, referring to a physical object rather than an abstract idea.
玦 combines 王 (jade) with 夬, which likely contributes the sound and may relate to the idea of a break or gap. The exact historical development is uncertain, but the character is used for a specific type of jade ornament.
The left side 王 (jade) and the right side 夬 (which looks like a broken or notched shape) together suggest a piece of jade that is incomplete or has a gap. Picture a jade ring with a visible break.
For ケツ, imagine a broken jade piece that looks like a small ketchup stain: ketchup -> ケツ, and the red stain marks the broken edge of the jade.