Stirring, rather than shaking, the Tongue Twister is significant because it gently combines the ingredients, preventing the drink from becoming overly aerated which can affect the texture and presentation. Stirring helps to maintain the clarity and integrity of the layered flavors, allowing the distinctive tastes of black and clear Sambuca, blackcurrant, and lime to emerge smoothly. This method ensures a balanced distribution of flavors without diluting the cocktail too much with melted ice.