side (of body), carry under arm
掖 centers on the side of the body, especially the area under the arm, and the action of carrying something tucked there.
掖 combines 扌 (hand) with 夜, which likely contributes the sound. The character is associated with the side of the body and the action of carrying under the arm, but the exact historical development is uncertain.
The hand radical 扌 beside 夜 suggests using your hand to hold something at your side, tucked under your arm like carrying a bundle at night.
For エキ, imagine carrying a heavy eki (駅, station) sign under your arm: eki -> エキ, and you're holding it at your side.