I installed a PD 4645 in our Class C last year. I also have an inverter directly connected to the batteries that shows the battery voltage. Here's my experience about how the converter works.
If the batteries have been discharged by running the furnace overnight and are down to say 12.4 volts, when the generator is started or shore power is plugged in, the green light on the converter fuse panel is on continuously and the battery voltage rises to about 14.4 volts after maybe an hour. The voltage stays at 14.4 volts for some period of time (not sure how long) then the charge wizard switches to 13.6 volts. When in this mode, the green light flashes rapidly. After some longer period of time (again not sure how long) the charge wizard goes into float mode with a voltage at the batteries of 13.2. In float mode, the green light has one quick flash at something like every 5-8 seconds.
Our RV is in the driveway and has been plugged in for at least a week, so the voltage when I checked just now is 13.2 and the light is flashing infrequently showing the charge wizard to be in float mode. When I pressed the button below the light, the light immediately came on steady and the battery voltage immediately went to 14.4. If I hold the button pressed for several seconds, the mode goes to the 13.6 voltage charge level and if I hold the button longer, the mode goes back to the float at 13.2 volts.
There is a white connector with four wires that connects the fuse panel to the charge wizard circuit. Since you aren't getting any action from the green light, perhaps this is missing or disconnected at either end. See picture.