So I noticed earlier that private ambulances were mentioned, especially AMR and McCormick and that they might be made if some reference images could be found. Recently I stumbled upon a Facebook page which disclosed that ambulances in owned by Medtrans (AMR Corporate), weren't using the name AMR across the board until the late 90s, instead just using the original names of the ambulance companies they bought. So I found a prominent one throughout Los Angeles County at the time and that being the Goodhew Ambulance company.
I'm not quite sure where the page got this info from but if you're still into the idea of private ambulances, I'll leave the link to it for you; https://www.facebook.com/NationalPrivateEMS/photos/goodhew-ambulanceearly-1900s-1993los-angeles-cafounded-by-j-h-goodhewacquired-by/10150698962387119/
Also another note from the Riverside Fire Department's Facebook page: https://www.facebook.com/CityOfRiversideFire/posts/today-in-rfd-history-december-1-1991goodhew-ambulance-places-into-service-med-83/2014236285382693/
Also some reference images
Apologies for the paragraph