Final answer:
The phlebotomy technician should have the patient dangle her arm for 1-2 minutes to allow gravity to pull blood into the veins and make them more visible.
Step-by-step explanation:
If a phlebotomy technician cannot find an apparent vein after applying a tourniquet, there are certain actions they can take. The correct action to take in this situation is option D: have the patient dangle her arm for 1-2 minutes. This allows gravity to pull blood into the veins, making them more visible and accessible.