I'm going to jump in with my thoughts here -
A couple of people (here and Facebook) have mentioned that you have the wrong (female) plug on the car - that is true if the outlet is a shoreline connector for a battery charger in the car (120V AC into the car), however, I believe what you have is a power outlet coming from the inverter in the car - (120V AC out), in order to run lights, an electric saw for extrication, etc. It should be simple enough to trace the wiring back inside the car to confirm (assuming either the inverter or on board charger are still in the car). The twist lock style connector also makes more sense for an outlet - as mentioned, if you used a twist lock for the shore power connection, and the ambulance crew is so excited to leave on a call that they forget to unplug the connection, you want something that will pull apart, to prevent damage. You would be more likely to want twist lock connection for the inverter output, so that as you're using the extrication saw, if you accidentally tug on the extension cord, it wouldn't come unplugged.

Above is a photo of a '73 S&S with both - output from the inverter on the left (twist lock, but only a two prong), and shore power on the right (recessed male plug).
My best guess on the matching plug is that (as Walter said) it is probably a manufacturer (Bell Electric Company) specific twist lock - pre- NEMA standardization for twist lock plugs. I don't know exactly when the NEMA standard for twist lock plugs was introduced, and I don't have any electrical catalogs that old. Bell is now a division of Hubbell, and I would imagine you will have to keep your eyes on Ebay for a vintage one if you really want to find a mate. If it were my car, and the inverter worked, and I wanted to be able to have a cord that plugged into it, I would take Paul's suggestion, and replace the outlet with a NEMA L5-15R (receptacle) and get a cord with a NEMA L5-15P (plug). It is rated for the same 15 amps at 120V AC as your current plug, and most people are not going to be able to tell the difference. It should work with your existing cover, so it will look the same externally.