trail, tow, drag, pull
曵 centers on pulling something along behind: trailing, towing, or dragging. The idea of pulling is the common thread across its meanings.
曵 is a variant of 曳, which combines 申 (to extend) with a dot, suggesting pulling or dragging something along. The exact historical development is uncertain, but it likely relates to the idea of extending or trailing.
The outer shape 曳 looks like a hand pulling a rope, and the extra dot inside is the object being dragged along behind. Together, 曵 means to trail or tow.
For エイ, imagine an 'A' frame being towed behind a truck: 'A' -> エイ, and the frame trails along the road.