MH lamps can cycle by the same process as HPS : voltage rise during life. Although the arc voltage does not rise so quickly as HPS, there is still some increase in life. There are two mechanisms. As the arc tube blackens during life, this causes its temperature to increase and that causes an increase in voltage. Similarly the electrodes burn back slightly and the increased arc gap increases the voltage - that effect is more significant with short arc and low power types.
But another mechanism is often more severe. During life some of the metals react with the quartz and are lost, leading to an increase in free iodine within the arc tube. If the lamp has an excellent hydrogen getter in the outer jacket this is no problem. But if not, or if the getter has become saturated over time, the tiny traces of hydrogen will diffuse into the arc tube and react with the iodine to form Hydrogen Iodide. This compound is extremely electronegative and increases the reignition peaks of the voltage waveform. As the arc tube runs up the HI vapour pressure begins to increase, and if sufficient is present it can steals enough electrons from the arc to cause the reignition peaks to rise to the level that the arc will extinguish.
You're a walking encyclopedia.
How on earth do you get all that information? General physics and chemistry applied to lighting? Or engineering documentation? Both maybe?