post, stake, axle
橛 centers on a sturdy vertical or horizontal structural piece: a wooden post driven into the ground, a stake, or an axle that supports a wheel.
橛 combines 木 (tree/wood) with 厥, which likely contributes the sound. The character originally referred to a wooden post or stake, and by extension an axle.
The left side 木 is wood, and the right side 厥 looks like a sturdy structure with a base. Picture a thick wooden post driven into the ground, or an axle made from a solid log.
For ケツ, imagine a wooden stake that is so tough it feels like solid ketsu (a made-up word for a hard, dense material). The ketsu sound cues ケツ while the stake stands firm.
something worthless; something impure; something unimportant; dried excrement in the shape of a stick