@Gary It is possible that the reason for there being a difference in the expected pump frequency is because doubling the fan speed doesn't necessarily equate to doubling the airflow. With regard to the program in the microcontroller it almost certainly uses one or more lookup tables and several algorithms which use the lookup table data and readings from the temperature sensor to arrive at the pump frequency:detected fan speed ratio. Ultimately these heaters are limited by the combustion air inlet cross-section, the area of the mesh that fuel can be evaporated from and the efficiency of the burner fan.

That's interesting, it as though the tach output functions as the clock signal for the pump.

It is fairly clear your pump is speeding up as you over ride the controller and speed the fan up, I wonder if that is common most of these type of heaters or just something more with just the one you have. I know some heater people found and open a calibration menu and there you set the fan speed and the hz the fuel pump runs at at the lowest setting then also at highest setting, and by adjusting these you can change the air fuel mix and the heater output. The settings between the heater adjust them base on the low and high so like 1/2 way it 1/2 between the to settings. I don't think the pump is firing every time magnets go by the sensor now if your turning it really slow then it may do that. What I think happening here is the controller is using math function base on numbers put in the calibration this give ratio how many turns of the fan per pulse of the pump, so if we had set the low cal 1hz and fan speed to 1000 rpm that would be 1000:1 ( now I just made up those numbers ) now the fan is going move less air per turn at higher RPM, so if we have high setting set to have the fan at 5000rpm then we maybe want the pump run at 3hz. Now this math function would work all RPMs between these to set points and it even lower or higher then the set points, so when your roller the fan over very slow by hand it may be 1:1 at that point. I done tuning work on EFI engines this type math functions are fairly common, and I betting there doing something like that here. But I can see how someone could think at the low setting that it going run pump at given setting and the fan at given setting and not have them link, and it could done that way, but then you need some code to check if fan turning and if at the right speed if not at right speed then you have code what do about it, by using a math function it will work even as the fan is changing speeds.

Does the controller error out when it senses the wrong RPM?