A third wheel makes sense, maybe consider placing it in the front with dynamic steering, so the wheels lean when they turn.
Overall I think the idea is interesting - I’ve seen ambulances get stuck in city traffic when cars have really no where to go and it takes precious time for them to figure it out. That being said here are some other things to consider:
-How often do ambulances get stuck, and their sirens ineffective?
-Often the patient riding is receiving care while in the ambulance. Will this still be a possibility in a narrow vehicle? Or is this vehicle for specific patients / situations?
Sounds awesome overall, good luck!