rouge, cosmetics
胭 centers on cosmetic coloring applied to the skin, especially rouge. The meaning extends naturally to cosmetics in general.
胭 combines ⺼ (flesh, body part) with 因, which likely contributes the sound. The character is associated with the throat or with rouge, but the exact historical development is uncertain.
The flesh component ⺼ suggests something applied to the body, and 因 can be thought of as a container. Picture a pot of rouge being dabbed onto the skin: 胭 is cosmetics.
For イン, imagine applying rouge inside an inn: inn -> イン, and the rouge colors your cheeks.