hairpin, crossbar of anchor, metal rod on sheath
笄 centers on a long, thin, pointed object used for fastening or securing: a hairpin, a crossbar on an anchor, or a metal rod on a sheath. The common thread is a slender, rigid piece that holds something in place.
笄 combines 竹 (bamboo) with 开, which likely contributes a phonetic element. The bamboo radical suggests the material of a hairpin or similar implement. The exact historical development of the lower component is uncertain.
The top 竹 (bamboo) suggests a slender bamboo tool, and the bottom 开 looks like a pointed rod with a crossbar. Picture a bamboo hairpin or a metal rod used to secure something.
For ケイ, imagine a hairpin shaped like the letter K: K -> ケイ, and the bamboo hairpin holds your hair in place.