to fit a handle into a socket, plug, cork
椊 centers on fitting one part snugly into another, like inserting a handle into a socket or plugging a hole with a cork.
椊 combines 木 (wood) with 卒, which likely contributes the sound. The character is associated with wooden fittings such as handles and plugs, but the exact historical development is uncertain.
A wooden 木 handle is fitted into a socket, like a soldier 卒 being slotted into a tight formation.
For ソツ, imagine a wooden plug that fits so snugly it makes a soft 'sots' sound when pushed in: sots -> ソツ.