Unmarked cop cars get all the respect they need from me because they use a simple, revolving light designed to get my attention not stun me into a fight or flight response.
I must admit, the only time I have seen an unmarked car with a simple revolving light is on Police Squad, Law & Order, and Homicide.
Every other unmarked car has a dash light, grill lights, and wigwags/headlight strobes, as well as a siren. not only that, but they also have strobes in the brake lights and reverse lights, and often on the rear deck.
If I were to hazard a guess, any cop that was only using a simple revolving light is probably in their personal car, with a cigarette plug so it can be removed easily and is only used on the rare times it's actually used.
Also, I can't speak for all states, but where I work, by state law it's either all or nothing. that means all lights on with an audible warning device, or none at all. there isn't any reduced intensity emergent response that you are talking about
Further, if you refuse to yield, that is your choice, but if they were going to help your family member in need, would you be the first person to be screaming that they took forever to get to the scene? I think it's grossly hypocritical for you to refuse to yield to a volunteer responder who is responding to a call (whether you agree with responses from home is irrelevant, as that is what the system uses), yet you will have them respond with lights and sirens in the ambulance to a call, and then judge them based on their response time.