I don't know if my BZ is three stage, but it most definitely has a float. It also has a two-stage charging circuit. Near the float voltage it backs off charging. The float light will flicker, but if there is lots of sun, it will go hard red and sit there until either the batteries voltage drops from a load or the sun goes down.
The final voltage is adjustable so it shouldn't matter what kind of battery you have. You can set it to cut off in the low 13's, or florce it as high as about 15.5.