neck of a garment, gusset, gore
袵 centers on parts of a garment near the neck or upper chest: the neckline, a gusset (a reinforcing piece), or a gore (a shaped panel). These are all structural fabric elements that shape the upper part of clothing.
袵 combines 衤 (clothing) with 任, which likely contributes the sound. The character refers to garment parts near the neck or upper body, but the exact historical development is uncertain.
The clothing radical 衤 beside 任 suggests a garment part that 'bears' or supports the neck area. Picture a tailor reinforcing the neckline with a gusset while someone wears the garment.
For ジン, imagine a tailor named Jin carefully sewing the neck of a garment: Jin -> ジン, and his needle shapes the gusset.
gusset (esp. in kimono); gore