tally, wooden pass
棨 centers on a physical token used for verification or passage: a tally or wooden pass that grants access or confirms identity.
棨 combines 木 (wood) with a phonetic component derived from 啓, suggesting a wooden object used as a pass or tally. The exact historical development is uncertain.
The bottom 木 shows it is made of wood, and the upper part looks like a gate or door being opened. Imagine a wooden pass that opens a gate: 棨 is a tally or wooden pass.
For ケイ, picture a wooden pass shaped like the letter K: K -> ケイ, and you use it to gain entry.