FOG is a mnemonic for the three emotional levers manipulators (including narcissists) pull to gain compliance: Fear, Obligation, and Guilt. Diagnosing which lever is active in a given exchange is the first step before applying a counter-response — see CAVA: Control, Approval, Validation, Attention (Manipulator Goals) for the paired framework on why the lever is being pulled, and Mirror Their Intentions, Not Their Actions for the core counter-strategy.
Source material (a "narcissist-neutralizing" toolkit video) pairs FOG with CAVA: Control, Approval, Validation, Attention (Manipulator Goals) as two halves of a diagnostic: FOG identifies the tactic, CAVA identifies the goal. The claimed value of naming the lever explicitly is that it exposes the manipulation without requiring an accusation — see Non-Confrontational Manipulation Countertactics Toolkit for the scripted responses built on this diagnosis.