Doug, I concur with Russell on some of that.
First, the siren isn't in the box, just so you know. The first push-button, as Russell said, was a brake for the mechanical siren (which would have been under the hood). That stops the siren from rotating, stopping the sound. The second would probably have been the "siren/horn" switch, which could have been a two-position switch, either siren or horn. This threw a relay which would allow you to use the horn button either for the horn or to run the siren. You would have had a switch for the beacon, one for the roof flashers that it looks like you may have had, and then.... I'd guess one was for the rear dome light.
The lights on the front may be "patient condition" lights. You may have switches in the back which would turn on a green, yellow, or red light on the dash, for the attendant to indicate to the driver how the patient was doing and/or whether he needed to put more foot into the gas! (I've never figured out why these lights were considered so important, why the attendant couldn't just yell, "Hey, Fred, step on it!")
The top of the switch box has lighted legends, essentially back-lit labels that show what each switch is for. It looks like those have been rubbed off but perhaps if you look closely or from the back, you can read what they are.
I've never seen switches on the side of the box, so I don't know why those are there.