lower part of face, jaw, gills of a fish
顋 centers on the lower facial area: the jaw and chin. The fish gill sense is a natural extension, as gills are the jaw-like structures on a fish's head.
顋 combines 思 (thought, but here likely a phonetic component) with 頁 (head), pointing to a part of the head. The exact historical role of 思 is uncertain, but the character consistently refers to the jaw or lower face.
Think of the head (頁) and the thoughtful (思) lower face: the jaw that moves when you ponder. 顋 is that jaw area.
For サイ, imagine a sigh (サイ) escaping from the jaw when you relax your lower face: sigh -> サイ.
fontanel; fontanelle