Head position and the constant monitoring of it are crucial for defense on bottom of half guard. Often, if your head moves too far in any direction, you are either vulnerable to guillotine chokes or the connection between your upper bodies is lost, which means your opponent can create space and take advantage of that space by establishing their own underhook or other problematic arm positioning.
The general idea is to keep your head either on your side of your opponent’s center line (the line which divides their torso vertically in half) or, should it cross that line, keep your head higher than their armpit and glued tightly to their body. Low and across the center line are sure-fire ways to get into guillotine trouble as well as giving your opponent a chance to push your head away from them. which would give them space to take away your advantage.