In real ambulances and police cars (fire engines probably too, but can't confirm) the switches for siren and blue light are separate, you'd turn on the blue light, and then toggle the siren with either a pedal or a switch on the dashboard. Nobody drives a call with the siren on all the time. Right now there is only one button (default m) that cycles through the different modes: off, blue light, and blue light + siren. This is not ideal, an really unimmersive. Two different buttons wouldn't be that hard to implement (i think) and, as an ambulance driver I'd love to see that changed in a future update (like flashing high beam, which is coming, I believe)
On the fire engine front (in the US at least), you usually have separate controls for the lights and electronic sirens similar to police cars and ambulances. The mechanical sirens (which are usually used alongside an electronic siren) have different controls, usually mounted on the floor of both the operator and officer's side (driver and passenger) with two switches, one for the siren and one for the siren brake. The mechanical sirens function similar to an engine, with a rotating disc that generates noise. Higher RPMs generate louder noises. The siren button increases the rpm and the brake is a literal brake for the rotating mechanism in the siren. Much like an engine, the siren decreases in loudness and pitch when you let off the siren button. This video is of a Federal Q2B, the standard siren on American fire apparatus. They do not use the brake in this video, but note the increases and decreases in loudness and pitch which are caused by pushing and letting go of the floor mounted button.
