The textbook teaches the critical path as a sequencing exercise: lay out the tasks, find the chain that decides the end date, protect it. That's correct and incomplete. In practice the critical path almost always runs through people, not tasks.
The task that gates everything is usually waiting on a decision only one person can make, or on a team that has three other things ranked above yours, or on an approval that sits in a queue. The Gantt chart shows a clean dependency. The real delay is a person who hasn't said yes yet.
So I track the critical path as people, not boxes. Who has to decide, who has to deliver, and what else is competing for their attention. That last part is the one the chart never shows and the one that actually slips dates. A dependency you're sure of can evaporate when the team behind it gets pulled onto a fire.
The practical move is to know your gating people by name, keep your work visible to them, and surface a stall the day it starts instead of the week it's discovered. The critical path doesn't break in the diagram. It breaks in someone's overloaded week.