path
逕 centers on a narrow or direct route: a path, lane, or shortcut. The extended senses of 'directly' and 'immediately' grow from the idea of taking a straight path.
逕 combines the movement radical 辶 with 巠, which likely contributes the sound and the idea of a straight or narrow line. The exact historical development of 巠 is uncertain.
The movement radical 辶 wraps around 巠, which looks like a series of narrow channels. Picture a winding footpath that cuts directly through the landscape.
For ケイ, imagine a narrow path shaped like the letter K: K -> ケイ, and you walk straight along it.