With so many other aspects of technique, load, and metabolic demand, it may be tempting to say,"who cares what my head is doing, I'm trying not to throw-up here."
But it does matter. In any movement your head and neck position should be a natural extension of your neutral spine. During the squat for example, it should appear that there is an eye bolt running from the tip of your head through your spine and out your sacrum. So, if your body tips forward, your head and neck will also tip forward in order to preserve that natural, vital positional relationship. Check out Coach A below.
Note that Coach A's gaze is actually 6-8 feet in front of him. Note also how ram rod straight his back is. Losing that neutral head position can trigger a cascade of bad movement. While the bio-mechanics are beyond the scope of this discussion, think of your head as one end of a sheet and your hips as the other end. We want this sheet pulled as tightly as possible during movement. Tilting your head back into cervical extension functionally lets the upper end of the sheet flap loosely in the wind, effectively making both ends unstable. When this happens we loose potential stability, strength, and power.
Keep your head in neutral and avoid the sneaky head fault.