Final answer:
In this situation, EMTs should quickly remove the external defibrillator vest and perform CPR to provide immediate life-saving measures.
Step-by-step explanation:
When EMTs arrive on the scene and find a pulseless and apneic patient wearing an external defibrillator vest, they should quickly remove the vest and perform CPR. The vest should be removed to ensure proper access to the patient's chest for effective CPR. CPR should be initiated immediately to provide essential oxygen and blood circulation until a defibrillator can be used.