distant place, remote, deep
夤 centers on remoteness and depth: a distant place, something far away, or a deep, profound state. The given meanings are loosely connected by the idea of being far removed in space or quality.
夤 is a rare character. It combines 夕 (evening) with 寅, which likely contributes the sound. The exact historical development is uncertain, and the character is not commonly used in modern Japanese.
The top 夕 suggests evening or darkness, and the bottom 寅 looks deep and complex. Imagine a distant, remote place growing dark and deep as evening falls.
For イン, picture an inn hidden in a deep, distant valley: inn -> イン, and the remote inn is hard to reach.