the handle of tools, tenon, cog
枘 centers on a projecting part that fits into a socket: a tenon in woodworking, a cog on a wheel, or the handle of a tool that inserts into a head.
枘 combines 木 (wood) with 內 (inside), suggesting a wooden part that goes inside another piece. The exact historical development is uncertain, but the component relationship fits the tenon/handle meaning.
The left side 木 is wood, and the right side 內 means inside. Picture a wooden tenon or tool handle that fits snugly inside a mortise or socket.
For ゼイ, imagine a wooden tenon that is slightly off, so you say 'it's zay' (like 'say' with a Z) as you adjust it: zay -> ゼイ, and the tenon slides into place.