Personal experience only, and may be wrong, and only applies to my particular heater.
The pulse pump has a coil that serves as an electromagnet to move a small plunger, so polarity PROBABLY won't matter.
My experience so far is that fuel/air mix is determined mainly by pulse pump frequency. The programmable models that allow for changing pump pulse frequency AND fan idle and maximum speeds are handy for efficient fuel burn.
It is a simple, think drool, fuel feed. There is no real pressure developed from the pump to the combustion chamber. Fuel oozes through the glow plug screen into the chamber. An impeller type fan forces air though shaped louvers to provide a swirl effect.
Even when you adjust min/max fuel pump frequency and min/max fan speeds, the controller adjusts those variables in the automatic thermostat settings as it ramps up and down. Mine does not shut down and restart. In automatic, it ramps up and down in pulses and fan speed.
In manual settings, it delivers constant pulses per second and fan speed.
By not shutting off and restarting automatically, battery consumption is reduced. The glow plug draws its 8-10 amps at every start AND stop. It is almost always more battery effective to allow the constant approximate one amp fan load, plus, constant burning helps keep things clean.
Since buying and installing mine, I've seen Chinese versions that supposedly have a barometric pressure sensor on the control board. That could be a plus if it works.