I would imagine the autism example is a case of general public knowledge of autism being poor; many people would assume that if you are speaking at all, you don't have any communication difficulties and they probably would not know why autism was relevant or what they should do differently.
It might be more effective, even though arguably not right, to say something like "I'm prone to panic attacks so please can you be gentle with me?"
If, just before saying "The ambulance is now on its way", the call-handler says "Now this is important: I do just need you to stay on the line for a little while longer, please", would most callers really still hang up?
I would think yes, because when somebody is in a panicked state, the brain centres that process language are not working very well, so they may literally not be taking in anything other than that confirmation they are looking for. That is probably why call handlers are trained to stick to asking direct, closed questions and simply repeating the question if someone doesn't give a useful answer.
The brain state that we go into when there is imminent threat/danger is much more instinctive and probably doesn't "understand" a telephone system very well - it's made for immediate, physical action with immediate, impactful consequences and not very much else makes sense. That's why your heart rate goes up and stuff like digestion stops because your body is diverting all your resources to allow you to do things like lift a car off a child, or fight a bear or whatever. While in normal situations you'd be disgusted and cautious to encounter vomit, you might launch in with your bare hands without thinking to clear a blockage from someone's airway or whatever.
If you know the system very well, and you have strong trust and understanding that behind the scenes while you're talking to this call handler, somebody else is lookng at all the current emergencies and status of all local ambulances and working to prioritise them all according to need and you trust the system that your call will get handled appropriately, then just making the call itself likely will meet that need even if you are panicking, and actually in a lot of cases of an emergency, there won't be a great deal that you can do, so providing information can feel (and be) useful enough to help calm that person back into rationality.
But in terms of your brain's reaction to "there is a threat, something very very bad is happening and can't stop it; I need assistance" phoning somebody up and waiting for a system to do its work (especially if you don't really know how it all works behind the scenes) doesn't really compute - your only goal is basically HELP THIS PERSON > GET ASSISTANCE and if you then feel like that goal is accomplished, you will immediately drop that action to focus on the next immediate action that will actually give you a real-time feedback and confirmation.