I built this voltage regulator a while back:
with the difference that I flipped the entire circuit's polarity to put the field switch "R4 is a feedback resistor that enhances the switching characteristics. When you decrease its resistance, switching occurs steeper, but the hysteresis window (i.e., the voltage that you need to reduce until the circuit switches back on) is larger. "Capacitor C1 stabilises the circuit at higher load. I have observed that the switching behaviour of the circuit without this capacitor is pretty "sharp" and stable if the load draws less than ca. 0.5 A (typically); however at higher current I observed a tendency to oscillate. This can be observed best with an oscilloscope, or a 12 V lamp as load: it will start to glow, instead of being switched completely on or completely off. C1 eliminates this instability; a value of 100 nF to 220 nF should do the job."
I built the circuit with a mosfet and observed the same effect -- at higher loads, instead of switching visibly on and off, the bulb in the test circuit dims.
I no longer have that bike and the voltage regulator I built, but it must have occupied a mental back burner all this time because I recently had an idea how to improve the circuit.
Although C1 alleviates the circuit's tendency to oscillate, it surely slows every on-off transition. It occured to me to reduce the value of R4 by an order of magnitude. Then move C1 from its location in the original circuit and put it in series with R4 instead.
The small value for R4 ought to sharpen switching enough to avoid the parasitic oscillation that characterized the original circuit.
Now, the presence of a capacitor in the feedback path will make the positive feedback transient. Using R4=10k and C4=0.1uF for example would result in a switching frequency on the order of 1 kHz (with sharper switching events than the original circuit).
During calibration one could leave out C1 and R4 and set the voltage in linear operation. Then install C1 and R4; and the circuit will oscillate around the setpoint.