Flexibility allows the face to show a very broad range of expressions. Think about Clint Eastwood’s stone-cold show-down face compared to Jim Carrey’s reaction expressions. Now there is range in flexibility.
The only problem is that their skulls are solid and do not change shape. Well, that might not be true for Mr. Carrey’s cranium, but let’s assume it is. A face is comprised of moving parts all related to one another working as an aesthetic team and is part of a larger team – the character.
Each team has a leader. The eyes are the first to act on internal orders or internal force and lead the face into action. If the eyes pinch shut, the entire face is probably pulled in toward them, forehead and eyebrows down with nose, cheeks, chin, and mouth drawn up - squash. When the eyes pop open the face is pushed away – stretch.
There will be exceptions, so note this as a 99% rule, not an absolute. For example, eyes close during a big inhale and eyebrows go up, not down toward the eyes. A face shows confinement and release of emotional energy, as does a hand or the entire body. The degree of flexibility in a face depends on the design and nature of the character in context to its world - is it cartooned or real?