If you mean trigger phrase like, "Hey Siri" I don't believe its possible on VAPI.
VAPI has strict BOT > USER > BOT... turn taking.
Prompt only affects LLM behavior, and LLMs don't really respond with empty strings. LLM does not decide if turn taking takes place or not. You can't prompt this.
As Kings said, try the start/stop speaking plans with different timing, make interruption 0.1s, but it will still talk if call is active and there's pause greater than your settings.