to stick into, to shake, put between, insert
搢 centers on the action of inserting or sticking something into a narrow space, often with a shaking or wedging motion. The meanings 'put between' and 'insert' are direct applications, while 'to shake' likely describes the motion used to work an object into place.
搢 combines 扌 (hand) with 晋, which likely contributes the sound and may relate to advancing or inserting. The exact historical development is uncertain.
The hand radical 扌 beside 晋 suggests a hand pushing something into a gap. Picture a hand shaking a peg to wedge it between two boards.
For シン, imagine inserting a thin shim into a crack: shim -> シン, and your hand shakes it into place.